Analysis in Geometry. By Danielle Long. Grade Level: 8 th. Time: 5-50 minute periods. Technology used: Geometer s sketchpad Geoboards NLVM website

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Analysis in Geometry. By Danielle Long. Grade Level: 8 th. Time: 5-50 minute periods. Technology used: Geometer s sketchpad Geoboards NLVM website"

Transcription

1 Analysis in Geometry By Danielle Long Grade Level: 8 th Time: 5-50 minute periods Technology used: Geometer s sketchpad Geoboards NLVM website 1

2 NCTM Standards Addressed Problem Solving Geometry Algebra Representation NYS Standards Addressed Standard 1 Mathematical Analysis Standard 2 Information Systems Standard 3 Mathematics 2

3 Sources Used South Western Math Matters2 an Integrated Approach, Lynch and Olmstead. Chapter 3, pgs , Copyright Materials Needed Geometer s Sketchpad Access to NLVM website Straws (3in, 5in, 8in, 12in) Geoboard Math Matters textbook, Chapter 3 pg

4 Overall Objective students will discover important concepts of geometry pertaining to triangles, parallel lines and polygons students will be able to identify angles formed by parallel lines and transversals students will use technology to discover triangle postulates Students will determine the properties of quadrilaterals. 4

5 Overview of the Unit Day 1 Exploring Parallel Lines and Transversals Discussion parallel lines Discovery of angle relationships Assignment in book Day 2 Classifying Triangles Creating triangles on the Geoboard Straw Activity Assignment in book Day 3 Classifying Quadrilaterals Drawing 4 sided figures Geoboard Activity/Worksheet What s My Name Worksheet? Day 4 Angle Sums Creating triangles in Geometer s Sketchpad Measuring angles in any triangle Sum of angles in any polygon Assignment in book. Day 5 Triangle Congruency Definition of Congruency Proving postulates using NLVM website Congruency Problems Assignment in the book 5

6 Day 1 Objective Students will identify angles formed by parallel lines and transversals. Opening activity. Students will be asked to give examples of where they see parallel lines in their everyday lives. Some possible answers: telephone poles, railroad tracks, and street maps. Classroom Activity. Students will be given a worksheet. The worksheet provided requires students to create a set of parallel lines and a transversal on Geometer s Sketchpad. Students may require step by step directions to create this sketch. Please refer to Appendix A for directions on GSP. The activity allows the student to use the technology to make connections about the angles formed in this diagram. The teacher should walk around the room and assist any students that are having difficulty with the technology or assignment. Closing Activity Allow 5-10 minutes at the end of class for a full class discussion. Students should share their discoveries with the class. A student might say all the obtuse angles in their diagram were equal. To make this connection stronger the teacher might ask some students to share their measurements for the obtuse angles. Then ask the students if all their obtuse angles were also equal. Since all the measurements are different and each student had the same conclusion the class should get a better understanding that this equivalency is not a fluke. The teacher should summarize the main idea of this activity by restating Every angle in this diagram has a relationship, either the angles are equal to each other or they add up to be 180 degrees. Homework pg All 6

7 Parallel Lines Sheet 1. Using GSP sketch a diagram of 2 parallel lines with a transversal through it. In the example below line A and B are parallel. 2. Label the diagram, and measure all angles. DIAGRAM 1 g Line A Line B h f b c a e d Draw and label the sketch you created in the space provided. 1.Line A and B are parallel to each other. Write out your own definition of what it means to be parallel. 2. What do you notice about all the obtuse angles? 3. What do you notice about all of the acute angle? 4. What is the sum of any obtuse angle and any acute angle on your diagram? 5. The interior angles are on the inside of the diagram they are: 7

8 6. The exterior angles are on the outside of the diagram they are: Alternate angles are non adjacent angles and are on opposite sides of the transversal. For example, in Diagram 1 Angle hfc and Angle fcd are examples of alternate interior angles. Write a statement that shows a relationship between alternate interior angles and alternate exterior angles 6. Write a statement about all the angles in this diagram. 8

9 Parallel Lines Sheet Answer Key 1. Using GSP sketch a diagram of 2 parallel lines with a transversal through it. In the example below line A and B are parallel. 2. Label the diagram, and measure all angles. Diagram 1 g Line A Line B h f b c a e d Draw and label the sketch you created in the space provided. f c e b d a g h 1.Line A and B are parallel to each other. Write out your own definition of what it means to be parallel. Parallel means that the lines will never cross, and they will always be the same distance apart. 2. What do you notice about all the obtuse angles? They are all equal to each other 3. What do you notice about all of the acute angle? 9

10 They are all equal to each other 4. What is the sum of any obtuse angle and any acute angle on this diagram? The sum equals The interior angles are on the inside of the diagram they are: (answers vary depending on how student labels their diagram) Angle bde, Angle deg, Angle ced, and Angle edh. The exterior angles are on the outside of the diagram they are: Angle feg, Angle fec, Angle adh, and Angle bda. Alternate angles are non adjacent angles and are on opposite sides of the transversal. For example, in Diagram 1 Angle hfc and Angle fcd are examples of alternate interior angles. Write a statement that shows a relationship between alternate interior angles and alternate exterior angles. Alternate interior angles are equal to each other. Alternate Exterior angles are also equal to each other. 6. Write a statement about all the angles in this diagram. Either 2 angles are equal to each other or they add up to be 180 degrees. 10

11 Day 2 Triangle Classification Objectives: Using Geoboards and straws students will be able to classify triangles according to their sides. Opening activity: Have students define the following terms isosceles triangles, scalene triangles, equilateral triangles, acute and obtuse angles. Have students share their responses with their classmates. Classroom Activity Students will be paired off and be given geoboards and rubber bands. Together with their partners students are asked to complete the geoboard worksheet. The time allowed will be 10 minutes. After this time is completed, the will discuss their findings. Important part of the discussion includes: What is the relationship between the smallest angle and the smallest side? How many obtuse angles can one triangle have? Students will be given 12 straws cut into 3in, 5 in, 8 in and 12 pieces. Students are to try and create triangles using the 4 different straws recording their results. Teacher should walk around the room making sure the results are being recorded. Students will be asked if they can find connection with the lengths of sides and triangles. (i.e. Why can t we make a triangle with 3, 5, 8 and we can make a triangle with 8, 12, and 3.) With some prompting students should recognize that the sum of any 2 sides of a triangle is greater than the third side. Allow minutes for this activity. Closing Students will do an exit pass explaining one new thing they learned about triangles and one thing they had already knew. Homework PG Try these 3-5 Exercise 1-4;

12 Geoboard Activity Use your geoboard to create the following triangles. Trace your solution on the dot pattern provided. Important questions to look at Where is the largest angle always located? The smallest? Is it possible to make a triangle that has more than one obtuse angle? Acute Isosceles Obtuse Scalene Right Isosceles Obtuse Isosceles Right Scalene Acute Scalene 12

13 Geoboard Activity Answer key Use your geoboard to create the following triangles. Trace your solution on the dot pattern provided. Important questions to look at Where is the largest angle always located? Across from the largest side The smallest? The smallest angle is across from the smallest side Acute Isosceles Obtuse Scalene Right Isosceles G H B Obtuse Isosceles Right Scalene Acute Scalene J I K 13

14 Lesson 3: Classifying Quadrilaterals Lesson Objectives: Students will be able to recognize a trapezoid, parallelogram, rhombus, rectangle, and square Students will be able to describe the properties of the figures above. Opening Activity: Have students draw a four sided figure. Classroom Activity 1. Tell the students that all the figures drawn in the class have one thing in common. That they are quadrilaterals. Ask the students if they can guess what it means to be a quadrilateral. Have them write their guess down, walk around the room to look at student s responses. Ask a student what their response was. It should be It has four sides 2. Show a picture of a parallelogram. Ask the students how many sets of parallel lines does the parallelogram have? Ask the students to write down the pairs of parallel lines. Ask the students if there are any sides that are equal, and what types of angles are there in this figure. 3. Students will be given out Quadrilateral Classification worksheets. Geoboards and dot paper. Students may work with their partners to complete the work. Go around the room and ask prompting questions about the figures. Such as, What do you notice the difference is between a rhombus and a square? What do they have in common? Once the students have completed the worksheets, review the answers on the overhead. Ask the students to go back through the worksheets and find out what each of the five special case quadrilaterals have in common and what are there differences. Students should be thinking about what is the difference between a square and a rhombus. Go around the room and ask prompting questions. Some questions to pose: Can a square also be a rectangle? Can a rectangle also be described as a parallelogram? Why or why not? Summarize and review the main point of the activity on the overhead. Closure: Ask the students to draw/or name all the four sided figures that have one set of parallel lines and have them hand it in before leaving. HMWK Have students complete what s my name worksheet. ` 14

15 Quadrilateral Classification On your geoboards create the following quadrilaterals and record your answers on the dot grids. Then describe the figures. Things you might want to consider are: Are any sides equal. If so which ones? What types of interior angles are there? Which sides are parallel, if any? Are there any interior angles that are equal to each other? (Use a corner of a piece of paper to measure angles) Parallelogram Description Square Description: 15

16 Rectangle Description Trapezoid Description Rhombus 16

17 Description 17

18 What s my name? I am a quadrilateral with exactly one pair of parallel lines. I am a quadrilateral with all sides equal, but no right angles I am a rhombus with all 4 angles congruent My diagonals are bisect each other and are perpendicular to each other. (Hint you want to draw the diagonals first then connect the points) ` 18

19 Quadrilateral Classification On your geoboards create the following quadrilaterals and record your answers on the dot grids. Then describe the figures. Things you might want to consider are: Are any sides equal. If so which ones? What types of interior angles are there? Which sides are parallel, if any? Are there any interior angles that are equal to each other? (Use a corner of a piece of paper to measure angles) Parallelogram Description There are 2 sets of sides that are parallel. Opposite angles are equal to each other. Square Description: All four sides and four angles are equal. There are 2 sides of lines that are parallel to each other. There are 4 right angles 19

20 Rectangle Description There are 4 right angles. Opposite sides are parallel and equal to each other. Trapezoid Description There is one set of parallel lines. Rhombus 20

21 Description All sides are equal. Opposite angles are equal. Opposite sides are parallel to each other. 21

22 What s my name? I am a quadrilateral with exactly one pair of parallel lines. Trapezoid I am a quadrilateral with all sides equal, but right no angles Rhombus I am a rhombus with all 4 angles congruent Square My diagonals are bisect each other and are perpendicular to each other. (Hint you want to draw the diagonals first then connect the points) Rhombus 22

23 Day 4 Triangle and Polygon Sums Objectives: Using GSP students will discover the sum of the angles of a triangle and other polygons Opening Activity Students will be asked to open up a new sketch in GSP and create a line. Classroom Activity Students will be using GSP to work on the Angle worksheet. Please refer to Appendix A for directions on creating triangles/ measuring angles on GSP. During the activity the teacher should be walking around the room to ensure the students are on task and asking any probing questions. Closing Activity Chart will be displayed on the overhead. Students will be asked if they found a pattern with the number of triangles that can be formed and the number of sides in any polygon. Students should respond that the number of triangles is always 2 less than the number of sides of the polygon. Homework Pg 99: 5-14 Pg

24 TRIANGLE SUMS Using Geometer's Sketchpad create a triangle and label it ABC. Use the measuring tool and measure the triangle s angles. Calculate the sum of all three angle measurements. Copy your findings in the space provided. a b.angle ABC= Angle BCA= Angle CAB= c Angle ABC+ Angle BCA +Angle CAB= Highlight point A and drag the point to a new position. (This should create a new triangle) What happened to the angle measurements? What happened to the sum? Can you create a triangle whose sum does not equal 180 degrees? Draw and label a 4 sided figure on Geometer s sketchpad. 24

25 Highlight 2 points that are diagonal from each other. Construct a segment. Recreate your sketch here What do you notice about the interior of this 4 sided figure? Using your knowledge of triangle, how many degrees are in any 4 sided figures? Use the measurement tool to prove your answer. Using Geometers sketchpad complete the chart below Name of Polygon Number of sides Number of Triangles Triangle 3 1 Quadrilateral 4 2 Pentagon 5 Hexagon 6 Heptagon 7 Octagon 8 Nonagon 9 Decagon 10 Degrees Do you notice a pattern between the number of triangles and the number of sides? How many degrees are in a polygon with 20 sides? 25

26 TRIANGLE SUMS Answer Key Using Geometer's Sketchpad create a triangle and label it ABC. Use the measuring tool and measure the triangle s angles. Calculate the sum of all three angle measurements. Copy your findings in the space provided. a b c m! a m! a m! c m! c Highlight point A and drag the point to a new position. (This should create a new triangle) What happened to the angle measurements? They Changed What happened to the sum? It is still 180. Can you create a triangle whose sum does not equal 180 degrees? NO Draw and label a 4 sided figure on Geometer s sketchpad. 26

27 a c b Highlight 2 points that are diagonal from each other. Construct a segment. Recreate your sketch here a P c b What do you notice about the interior of this 4 sided figure? It creates 2 triangles. Using your knowledge of triangle, how many degrees are in any 4 sided figures? 360 degrees. Use the measurement tool to prove your answer. m! c m! c m! a m! a m! a 27

28 Using Geometers sketchpad complete the chart below Name of Polygon Number of sides Number of Triangles Degrees Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Decagon Do you notice a pattern between the number of triangles and the number of sides? Yes. The number of triangles is always 2 less than the number of sides How many degrees are in a polygon with 20 sides? There would be 18 triangles so 18*180=3240 degrees. 28

29 Day 5 Triangle Congruency Objective: students will be able to identify congruent triangles. Opening Activity Students will be asked to define congruent. Classroom Activity Students will log onto the internet and NLVM website. Students will be asked to go to Geometry, grades 6-8 and click on congruent triangles. Using NLVM website and the worksheet students will work with SSS, SAS and ASA Postulates to gain a better understanding of why they prove triangle congruencies. Allow minutes for this activity. Students should discuss with the class the answers to the worksheet. The teacher will then put up examples from the book, pg 104 Try these 1-4 and ask the students to apply their knowledge to answer which triangles are congruent and why. Homework pg ALL 29

30 Triangle Congruency In SSS, each blue segment was equal to each red segment. What happened when you formed the blue and red triangle? Was it possible to have the red triangle not congruent to the blue triangle? Why or Why Not? In SAS each blue segment was equal to the red segments and the blue angle was equal to the red angle. After fitting both the red segments onto the red angle, why do you think it automatically formed a triangle? How does this show that if 2 triangles have 2 sides and the include angle equal they are congruent to each other? ASA means that if two triangles have 2 equal angles and the included side is also equal then the triangles must be congruent. How were you able to show this using the technology? 30

31 Triangle Congruency In SSS, each blue segment was equal to each red segment. What happened when you formed the blue and red triangle? Was it possible to have the red triangle not congruent to the blue triangle? Why or Why Not? Both of the triangles were equal. No it is not possible. All three segments would only fit together one way to form a triangle. In SAS each blue segment was equal to the red segments and the blue angle was equal to the red angle. After fitting both the red segments onto the red angle, why do you think it automatically formed a triangle? Because the there is only one line segment that would connect the two endpoints of the 2 segments How does this show that if 2 triangles have 2 sides and the include angle equal they are congruent to each other? There is only one triangle that can be formed when you have 2 sides and the included angle already given. Therefore if another triangle has the same 2 sides and included angle that new triangle must be congruent to the first. ASA means that if two triangles have 2 equal angles and the included side is also equal then the triangles must be congruent. How were you able to show this using the technology? When building the triangle the line segment had to fit onto the angle ray of each of the 2 angles given. The rays not used are going opposite directions and they will meet at one point only. Meaning the lengths of the other 2 sides is determined by this one point. Therefore if 2 triangles have 2 equal angles and the included side is also equal the triangles must be congruent. 31

32 Appendix A GUIDE TO GSP ACTIVITIES Directions for Geometer s Sketchpad Remember when working with Sketchpad, often an error occurs when incorrect information is highlighted. Parallel Lines Using the line tool construct a line. Use the pointer tool to highlight the line. Go up to Transform, Choose Translate. Parallel Lines with a Transversal Follow the procedure for parallel lines above. Using the point tool place a point on each of the lines. Highlight the points. Go up to Construct, choose line. Naming the Angles: an angle is made up of 3 points. Using the case above, additional points must be added to the line in order for an angle to be named. Using the point tool place points on the lines. Then go up to display, choose label points. This will automatically label all points on the lines. 32

33 L E F K I J G H Directions for Measuring Angles In order to measure angles you must click on three points. For instance, if measuring Angle LEF first highlight point L then point F then point E. Go up to Measure, choose angle. To Measure angle LFK repeat steps only first highlight L then F then K. In order to find the sum of the angles, go up to Measure, choose calculate and click on values and choose the measurements you would like to include in your sum. m! L m! L m! L L E F K I J G H Directions to create a triangle on Geometer s Sketchpad. Using the pointer tool, make three points. Use the arrow tool and highlight each point. Go up to the menu, Construct then choose Segments. This will create a triangle. To Label the triangle highlight the points choose Display and Label Points. l l 1 m n m n

34 Measure a triangle angles. If measuring Angle 123 in the triangle click on 1 then 2 then 3. Select Measure then Angle To measure angle 231 click on 2 then 3 then 1. To calculate the sum of all the angles in the triangle, Select Calculate, then click on the angle measures you would like to include. 34

11.3 Curves, Polygons and Symmetry

11.3 Curves, Polygons and Symmetry 11.3 Curves, Polygons and Symmetry Polygons Simple Definition A shape is simple if it doesn t cross itself, except maybe at the endpoints. Closed Definition A shape is closed if the endpoints meet. Polygon

More information

Unit 6 Grade 7 Geometry

Unit 6 Grade 7 Geometry Unit 6 Grade 7 Geometry Lesson Outline BIG PICTURE Students will: investigate geometric properties of triangles, quadrilaterals, and prisms; develop an understanding of similarity and congruence. Day Lesson

More information

Line. A straight path that continues forever in both directions.

Line. A straight path that continues forever in both directions. Geometry Vocabulary Line A straight path that continues forever in both directions. Endpoint A point that STOPS a line from continuing forever, it is a point at the end of a line segment or ray. Ray A

More information

Geometry. Unit 6. Quadrilaterals. Unit 6

Geometry. Unit 6. Quadrilaterals. Unit 6 Geometry Quadrilaterals Properties of Polygons Formed by three or more consecutive segments. The segments form the sides of the polygon. Each side intersects two other sides at its endpoints. The intersections

More information

EXPLORING GEOMETRIC FIGURES Grade 10 6-Day Lesson Plan

EXPLORING GEOMETRIC FIGURES Grade 10 6-Day Lesson Plan 1 EXPLORING GEOMETRIC FIGURES Grade 10 6-Day Lesson Plan Tangrams Geoboards Equation Grapher Green Globs AlphaShapes Protractor Compass Created by Sandra Metzler 2 OVERALL OBJECTIVES 1- Students will increase

More information

Quadrilaterals Properties of a parallelogram, a rectangle, a rhombus, a square, and a trapezoid

Quadrilaterals Properties of a parallelogram, a rectangle, a rhombus, a square, and a trapezoid Quadrilaterals Properties of a parallelogram, a rectangle, a rhombus, a square, and a trapezoid Grade level: 10 Prerequisite knowledge: Students have studied triangle congruences, perpendicular lines,

More information

A convex polygon is a polygon such that no line containing a side of the polygon will contain a point in the interior of the polygon.

A convex polygon is a polygon such that no line containing a side of the polygon will contain a point in the interior of the polygon. hapter 7 Polygons A polygon can be described by two conditions: 1. No two segments with a common endpoint are collinear. 2. Each segment intersects exactly two other segments, but only on the endpoints.

More information

Target To know the properties of a rectangle

Target To know the properties of a rectangle Target To know the properties of a rectangle (1) A rectangle is a 3-D shape. (2) A rectangle is the same as an oblong. (3) A rectangle is a quadrilateral. (4) Rectangles have four equal sides. (5) Rectangles

More information

Unit 8. Quadrilaterals. Academic Geometry Spring Name Teacher Period

Unit 8. Quadrilaterals. Academic Geometry Spring Name Teacher Period Unit 8 Quadrilaterals Academic Geometry Spring 2014 Name Teacher Period 1 2 3 Unit 8 at a glance Quadrilaterals This unit focuses on revisiting prior knowledge of polygons and extends to formulate, test,

More information

Lesson 28: Properties of Parallelograms

Lesson 28: Properties of Parallelograms Student Outcomes Students complete proofs that incorporate properties of parallelograms. Lesson Notes Throughout this module, we have seen the theme of building new facts with the use of established ones.

More information

Unit 6 Grade 7 Geometry

Unit 6 Grade 7 Geometry Unit 6 Grade 7 Geometry Lesson Outline BIG PICTURE Students will: investigate geometric properties of triangles, quadrilaterals, and prisms; develop an understanding of similarity and congruence. Day Lesson

More information

Unit 8 Grade 7 Similarity, Congruency, and Transformations

Unit 8 Grade 7 Similarity, Congruency, and Transformations Unit 8 Grade 7 Similarity, Congruency, and Transformations Lesson Outline BIG PICTURE Students will: understand location using four quadrants of the coordinate axis; investigate and apply transformations

More information

Unit 3: Triangle Bisectors and Quadrilaterals

Unit 3: Triangle Bisectors and Quadrilaterals Unit 3: Triangle Bisectors and Quadrilaterals Unit Objectives Identify triangle bisectors Compare measurements of a triangle Utilize the triangle inequality theorem Classify Polygons Apply the properties

More information

parallel lines perpendicular lines intersecting lines vertices lines that stay same distance from each other forever and never intersect

parallel lines perpendicular lines intersecting lines vertices lines that stay same distance from each other forever and never intersect parallel lines lines that stay same distance from each other forever and never intersect perpendicular lines lines that cross at a point and form 90 angles intersecting lines vertices lines that cross

More information

G7-3 Measuring and Drawing Angles and Triangles Pages

G7-3 Measuring and Drawing Angles and Triangles Pages G7-3 Measuring and Drawing Angles and Triangles Pages 102 104 Curriculum Expectations Ontario: 5m51, 5m52, 5m54, 6m48, 6m49, 7m3, 7m4, 7m46 WNCP: 6SS1, review, [T, R, V] Vocabulary angle vertex arms acute

More information

8-2 Classifying Angles Objective: Identify different types of angles Explain how to determine the type of angle.

8-2 Classifying Angles Objective: Identify different types of angles Explain how to determine the type of angle. 8-1 Classifying Lines Objective: Identify type of lines and line relationships Language Objective: Classify and then justify your classification Vocabulary: line- continues in both directions for ever

More information

Grade 3 Core Standard III Assessment

Grade 3 Core Standard III Assessment Grade 3 Core Standard III Assessment Geometry and Measurement Name: Date: 3.3.1 Identify right angles in two-dimensional shapes and determine if angles are greater than or less than a right angle (obtuse

More information

Intermediate Math Circles October 10, 2012 Geometry I: Angles

Intermediate Math Circles October 10, 2012 Geometry I: Angles Intermediate Math Circles October 10, 2012 Geometry I: Angles Over the next four weeks, we will look at several geometry topics. Some of the topics may be familiar to you while others, for most of you,

More information

Geometry Concepts. Figures that lie in a plane are called plane figures. These are all plane figures. Triangle 3

Geometry Concepts. Figures that lie in a plane are called plane figures. These are all plane figures. Triangle 3 Geometry Concepts Figures that lie in a plane are called plane figures. These are all plane figures. Polygon No. of Sides Drawing Triangle 3 A polygon is a plane closed figure determined by three or more

More information

Geometry and Measurement

Geometry and Measurement Geometry and Measurement (Developmentally Appropriate Lessons for K-5 Students) Amanda Anderson Title I Teacher Lincoln Elementary aanderson@bemidji.k12.mn.us Executive Summary This 10-day unit plan is

More information

Chapter Three. Parallel Lines and Planes

Chapter Three. Parallel Lines and Planes Chapter Three Parallel Lines and Planes Objectives A. Use the terms defined in the chapter correctly. B. Properly use and interpret the symbols for the terms and concepts in this chapter. C. Appropriately

More information

1 of 69 Boardworks Ltd 2004

1 of 69 Boardworks Ltd 2004 1 of 69 2 of 69 Intersecting lines 3 of 69 Vertically opposite angles When two lines intersect, two pairs of vertically opposite angles are formed. a d b c a = c and b = d Vertically opposite angles are

More information

LEVEL G, SKILL 1. Answers Be sure to show all work.. Leave answers in terms of ϖ where applicable.

LEVEL G, SKILL 1. Answers Be sure to show all work.. Leave answers in terms of ϖ where applicable. Name LEVEL G, SKILL 1 Class Be sure to show all work.. Leave answers in terms of ϖ where applicable. 1. What is the area of a triangle with a base of 4 cm and a height of 6 cm? 2. What is the sum of the

More information

UNIT H1 Angles and Symmetry Activities

UNIT H1 Angles and Symmetry Activities UNIT H1 Angles and Symmetry Activities Activities H1.1 Lines of Symmetry H1.2 Rotational and Line Symmetry H1.3 Symmetry of Regular Polygons H1.4 Interior Angles in Polygons Notes and Solutions (1 page)

More information

15 Polygons. 15.1 Angle Facts. Example 1. Solution. Example 2. Solution

15 Polygons. 15.1 Angle Facts. Example 1. Solution. Example 2. Solution 15 Polygons MEP Y8 Practice Book B 15.1 Angle Facts In this section we revise some asic work with angles, and egin y using the three rules listed elow: The angles at a point add up to 360, e.g. a c a +

More information

Geometry and Measurement

Geometry and Measurement Geometry and Measurement 7 th Grade Math Michael Hepola Henning Public School mhepola@henning.k12.mn.us Executive Summary This 12-day unit is constructed with the idea of teaching this geometry section

More information

Lesson 1: Exploring Polygons

Lesson 1: Exploring Polygons Lesson 1: Exploring Polygons Objectives: Students will be able to identify whether a given shape is a polygon using the properties of polygons. Students will be able to identify and name polygons that

More information

*1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles.

*1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles. Students: 1. Students understand and compute volumes and areas of simple objects. *1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles. Review

More information

UNCORRECTED PROOF. Unit objectives. Website links Opener Online angle puzzles 2.5 Geometry resources, including interactive explanations

UNCORRECTED PROOF. Unit objectives. Website links Opener Online angle puzzles 2.5 Geometry resources, including interactive explanations 21.1 Sequences Get in line Unit objectives Understand a proof that the angle sum of a triangle is 180 and of a quadrilateral is 360 ; and the exterior angle of a triangle is equal to the sum of the two

More information

INFORMATION FOR TEACHERS

INFORMATION FOR TEACHERS INFORMATION FOR TEACHERS The math behind DragonBox Elements - explore the elements of geometry - Includes exercises and topics for discussion General information DragonBox Elements Teaches geometry through

More information

Grade 5 supplement. Set C1 Geometry: Triangles & Quadrilaterals. Includes. Skills & Concepts

Grade 5 supplement. Set C1 Geometry: Triangles & Quadrilaterals. Includes. Skills & Concepts Grade 5 supplement Set C1 Geometry: Triangles & Quadrilaterals Includes Activity 1: Classifying Triangles C1.1 Activity 2: Sorting & Classifying Quadrilaterals C1.13 Activity 3: Finding the Perimeter &

More information

Activity Set 4. Trainer Guide

Activity Set 4. Trainer Guide Geometry and Measurement of Plane Figures Activity Set 4 Trainer Guide Int_PGe_04_TG GEOMETRY AND MEASUREMENT OF PLANE FIGURES Activity Set #4 NGSSS 3.G.3.1 NGSSS 3.G.3.3 NGSSS 4.G.5.1 NGSSS 5.G.3.1 Amazing

More information

Angles that are between parallel lines, but on opposite sides of a transversal.

Angles that are between parallel lines, but on opposite sides of a transversal. GLOSSARY Appendix A Appendix A: Glossary Acute Angle An angle that measures less than 90. Acute Triangle Alternate Angles A triangle that has three acute angles. Angles that are between parallel lines,

More information

Polygons are figures created from segments that do not intersect at any points other than their endpoints.

Polygons are figures created from segments that do not intersect at any points other than their endpoints. Unit #5 Lesson #1: Polygons and Their Angles. Polygons are figures created from segments that do not intersect at any points other than their endpoints. A polygon is convex if all of the interior angles

More information

E XPLORING QUADRILATERALS

E XPLORING QUADRILATERALS E XPLORING QUADRILATERALS E 1 Geometry State Goal 9: Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space. Statement of Purpose: The activities in this

More information

Geometry Progress Ladder

Geometry Progress Ladder Geometry Progress Ladder Maths Makes Sense Foundation End-of-year objectives page 2 Maths Makes Sense 1 2 End-of-block objectives page 3 Maths Makes Sense 3 4 End-of-block objectives page 4 Maths Makes

More information

Geometry of 2D Shapes

Geometry of 2D Shapes Name: Geometry of 2D Shapes Answer these questions in your class workbook: 1. Give the definitions of each of the following shapes and draw an example of each one: a) equilateral triangle b) isosceles

More information

2. Sketch and label two different isosceles triangles with perimeter 4a + b. 3. Sketch an isosceles acute triangle with base AC and vertex angle B.

2. Sketch and label two different isosceles triangles with perimeter 4a + b. 3. Sketch an isosceles acute triangle with base AC and vertex angle B. Section 1.5 Triangles Notes Goal of the lesson: Explore the properties of triangles using Geometer s Sketchpad Define and classify triangles and their related parts Practice writing more definitions Learn

More information

Sum of the interior angles of a n-sided Polygon = (n-2) 180

Sum of the interior angles of a n-sided Polygon = (n-2) 180 5.1 Interior angles of a polygon Sides 3 4 5 6 n Number of Triangles 1 Sum of interiorangles 180 Sum of the interior angles of a n-sided Polygon = (n-2) 180 What you need to know: How to use the formula

More information

Overview of Geometry Map Project

Overview of Geometry Map Project Overview of Geometry Map Project The goal: To demonstrate your understanding of geometric vocabulary, you will be designing and drawing a town map that incorporates many geometric key terms. The project

More information

Third Grade Shapes Up! Grade Level: Third Grade Written by: Jill Pisman, St. Mary s School East Moline, Illinois Length of Unit: Eight Lessons

Third Grade Shapes Up! Grade Level: Third Grade Written by: Jill Pisman, St. Mary s School East Moline, Illinois Length of Unit: Eight Lessons Third Grade Shapes Up! Grade Level: Third Grade Written by: Jill Pisman, St. Mary s School East Moline, Illinois Length of Unit: Eight Lessons I. ABSTRACT This unit contains lessons that focus on geometric

More information

Grade 8 Mathematics Geometry: Lesson 2

Grade 8 Mathematics Geometry: Lesson 2 Grade 8 Mathematics Geometry: Lesson 2 Read aloud to the students the material that is printed in boldface type inside the boxes. Information in regular type inside the boxes and all information outside

More information

SFUSD Mathematics Core Curriculum Development Project

SFUSD Mathematics Core Curriculum Development Project 1 SFUSD Mathematics Core Curriculum Development Project 2014 2015 Creating meaningful transformation in mathematics education Developing learners who are independent, assertive constructors of their own

More information

Chapter 1: Essentials of Geometry

Chapter 1: Essentials of Geometry Section Section Title 1.1 Identify Points, Lines, and Planes 1.2 Use Segments and Congruence 1.3 Use Midpoint and Distance Formulas Chapter 1: Essentials of Geometry Learning Targets I Can 1. Identify,

More information

**The Ruler Postulate guarantees that you can measure any segment. **The Protractor Postulate guarantees that you can measure any angle.

**The Ruler Postulate guarantees that you can measure any segment. **The Protractor Postulate guarantees that you can measure any angle. Geometry Week 7 Sec 4.2 to 4.5 section 4.2 **The Ruler Postulate guarantees that you can measure any segment. **The Protractor Postulate guarantees that you can measure any angle. Protractor Postulate:

More information

Constructing Symmetrical Shapes

Constructing Symmetrical Shapes 07-NEM5-WBAns-CH07 7/20/04 4:36 PM Page 62 1 Constructing Symmetrical Shapes 1 Construct 2-D shapes with one line of symmetry A line of symmetry may be horizontal or vertical 2 a) Use symmetry to complete

More information

Properties of Polygons Objective To explore the geometric properties of polygons.

Properties of Polygons Objective To explore the geometric properties of polygons. Properties of Polygons Objective To explore the geometric properties of polygons. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment

More information

LESSON PLAN #1: Discover a Relationship

LESSON PLAN #1: Discover a Relationship LESSON PLAN #1: Discover a Relationship Name Alessandro Sarra Date 4/14/03 Content Area Math A Unit Topic Coordinate Geometry Today s Lesson Sum of the Interior Angles of a Polygon Grade Level 9 NYS Mathematics,

More information

Grade 6 Math Circles Winter February 24/25. Angle

Grade 6 Math Circles Winter February 24/25. Angle Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grade 6 Math Circles Winter 2015 - February 24/25 Angles Introduction At this point in your mathematical

More information

Honors Packet on. Polygons, Quadrilaterals, and Special Parallelograms

Honors Packet on. Polygons, Quadrilaterals, and Special Parallelograms Honors Packet on Polygons, Quadrilaterals, and Special Parallelograms Table of Contents DAY 1: (Ch. 6-1) SWBAT: Find measures of interior and exterior angles of polygons Pgs: #1 6 in packet HW: Pages 386

More information

Check students drawings. GNL or LNG

Check students drawings. GNL or LNG 8-1 Draw each geometric figure. Check students drawings. 1. a point 2. a ray 3. an angle 4. the angle shown. GNL or LNG G Look at the angles below. N L P M A V 5. Which angles are right angles? 6. Which

More information

Upper Elementary Geometry

Upper Elementary Geometry Upper Elementary Geometry Geometry Task Cards Answer Key The unlicensed photocopying, reproduction, display, or projection of the material, contained or accompanying this publication, is expressly prohibited

More information

Unit 8. Ch. 8. "More than three Sides"

Unit 8. Ch. 8. More than three Sides Unit 8. Ch. 8. "More than three Sides" 1. Use a straightedge to draw CONVEX polygons with 4, 5, 6 and 7 sides. 2. In each draw all of the diagonals from ONLY ONE VERTEX. A diagonal is a segment that joins

More information

Estimating Angle Measures

Estimating Angle Measures 1 Estimating Angle Measures Compare and estimate angle measures. You will need a protractor. 1. Estimate the size of each angle. a) c) You can estimate the size of an angle by comparing it to an angle

More information

Lesson 6: Polygons and Angles

Lesson 6: Polygons and Angles Lesson 6: Polygons and Angles Selected Content Standards Benchmark Assessed: G.4 Using inductive reasoning to predict, discover, and apply geometric properties and relationships (e.g., patty paper constructions,

More information

Math 6: Unit 7: Geometry Notes 2-Dimensional Figures

Math 6: Unit 7: Geometry Notes 2-Dimensional Figures Math 6: Unit 7: Geometry Notes -Dimensional Figures Prep for 6.G.A.1 Classifying Polygons A polygon is defined as a closed geometric figure formed by connecting line segments endpoint to endpoint. Polygons

More information

TImath.com. Geometry. Triangle Sides & Angles

TImath.com. Geometry. Triangle Sides & Angles Triangle Sides & Angles ID: 8792 Time required 40 minutes Activity Overview In this activity, students will explore side and angle relationships in a triangle. First, students will discover where the longest

More information

Date: Period: Symmetry

Date: Period: Symmetry Name: Date: Period: Symmetry 1) Line Symmetry: A line of symmetry not only cuts a figure in, it creates a mirror image. In order to determine if a figure has line symmetry, a figure can be divided into

More information

11-5 Polygons ANSWER: ANSWER: ANSWER:

11-5 Polygons ANSWER: ANSWER: ANSWER: Determine whether the figure is a polygon. If it is, classify the polygon. If it is not a polygon, explain why. 1. 5. KALEIDOSCOPE The kaleidoscope image shown is a regular polygon with 14 sides. What

More information

The Polygon Angle-Sum Theorems

The Polygon Angle-Sum Theorems 6-1 The Polygon Angle-Sum Theorems Common Core State Standards G-SRT.B.5 Use congruence... criteria to solve problems and prove relationships in geometric figures. MP 1, MP 3 Objectives To find the sum

More information

Geometry. Geometry is the study of shapes and sizes. The next few pages will review some basic geometry facts. Enjoy the short lesson on geometry.

Geometry. Geometry is the study of shapes and sizes. The next few pages will review some basic geometry facts. Enjoy the short lesson on geometry. Geometry Introduction: We live in a world of shapes and figures. Objects around us have length, width and height. They also occupy space. On the job, many times people make decision about what they know

More information

1. An isosceles trapezoid does not have perpendicular diagonals, and a rectangle and a rhombus are both parallelograms.

1. An isosceles trapezoid does not have perpendicular diagonals, and a rectangle and a rhombus are both parallelograms. Quadrilaterals - Answers 1. A 2. C 3. A 4. C 5. C 6. B 7. B 8. B 9. B 10. C 11. D 12. B 13. A 14. C 15. D Quadrilaterals - Explanations 1. An isosceles trapezoid does not have perpendicular diagonals,

More information

Unit 6 Geometry: Constructing Triangles and Scale Drawings

Unit 6 Geometry: Constructing Triangles and Scale Drawings Unit 6 Geometry: Constructing Triangles and Scale Drawings Introduction In this unit, students will construct triangles from three measures of sides and/or angles, and will decide whether given conditions

More information

7.3 & 7.4 Polygon Formulas completed.notebook January 10, 2014

7.3 & 7.4 Polygon Formulas completed.notebook January 10, 2014 Chapter 7 Polygons Polygon 1. Closed Figure # of Sides Polygon Name 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 2. Straight sides/edges 7 Heptagon 8 Octagon 9 Nonagon 10 Decagon 12 Dodecagon 15 Pentadecagon

More information

The angle sum property of triangles can help determine the sum of the measures of interior angles of other polygons.

The angle sum property of triangles can help determine the sum of the measures of interior angles of other polygons. Interior Angles of Polygons The angle sum property of triangles can help determine the sum of the measures of interior angles of other polygons. The sum of the measures of the interior angles of a triangle

More information

Name: 22K 14A 12T /48 MPM1D Unit 7 Review True/False (4K) Indicate whether the statement is true or false. Show your work

Name: 22K 14A 12T /48 MPM1D Unit 7 Review True/False (4K) Indicate whether the statement is true or false. Show your work Name: _ 22K 14A 12T /48 MPM1D Unit 7 Review True/False (4K) Indicate whether the statement is true or false. Show your work 1. An equilateral triangle always has three 60 interior angles. 2. A line segment

More information

POLYGONS

POLYGONS POLYGONS 8.1.1 8.1.5 After studying triangles and quadrilaterals, students now extend their study to all polygons. A polygon is a closed, two-dimensional figure made of three or more nonintersecting straight

More information

Pythagorean Theorem. Inquiry Based Unit Plan

Pythagorean Theorem. Inquiry Based Unit Plan Pythagorean Theorem Inquiry Based Unit Plan By: Renee Carey Grade: 8 Time: 5 days Tools: Geoboards, Calculators, Computers (Geometer s Sketchpad), Overhead projector, Pythagorean squares and triangle manipulatives,

More information

SHAPE, SPACE AND MEASURES

SHAPE, SPACE AND MEASURES SHAPE, SPACE AND MEASURES Pupils should be taught to: Use accurately the vocabulary, notation and labelling conventions for lines, angles and shapes; distinguish between conventions, facts, definitions

More information

Shape and Space. General Curriculum Outcome E: Students will demonstrate spatial sense and apply geometric concepts, properties and relationships.

Shape and Space. General Curriculum Outcome E: Students will demonstrate spatial sense and apply geometric concepts, properties and relationships. Shape and Space General Curriculum Outcome E: Students will demonstrate spatial sense and apply geometric concepts, properties and relationships. Elaboration Instructional Strategies/Suggestions KSCO:

More information

Grade 4 - Module 4: Angle Measure and Plane Figures

Grade 4 - Module 4: Angle Measure and Plane Figures Grade 4 - Module 4: Angle Measure and Plane Figures Acute angle (angle with a measure of less than 90 degrees) Angle (union of two different rays sharing a common vertex) Complementary angles (two angles

More information

PROPERTIES OF TRIANGLES AND QUADRILATERALS

PROPERTIES OF TRIANGLES AND QUADRILATERALS Mathematics Revision Guides Properties of Triangles, Quadrilaterals and Polygons Page 1 of 21 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Higher Tier PROPERTIES OF TRIANGLES AND QUADRILATERALS

More information

Situation: Proving Quadrilaterals in the Coordinate Plane

Situation: Proving Quadrilaterals in the Coordinate Plane Situation: Proving Quadrilaterals in the Coordinate Plane 1 Prepared at the University of Georgia EMAT 6500 Date Last Revised: 07/31/013 Michael Ferra Prompt A teacher in a high school Coordinate Algebra

More information

Geometry Vocabulary Booklet

Geometry Vocabulary Booklet Geometry Vocabulary Booklet Geometry Vocabulary Word Everyday Expression Example Acute An angle less than 90 degrees. Adjacent Lying next to each other. Array Numbers, letter or shapes arranged in a rectangular

More information

Chapters 4 and 5 Notes: Quadrilaterals and Similar Triangles

Chapters 4 and 5 Notes: Quadrilaterals and Similar Triangles Chapters 4 and 5 Notes: Quadrilaterals and Similar Triangles IMPORTANT TERMS AND DEFINITIONS parallelogram rectangle square rhombus A quadrilateral is a polygon that has four sides. A parallelogram is

More information

Properties of Special Parallelograms

Properties of Special Parallelograms Properties of Special Parallelograms Lab Summary: This lab consists of four activities that lead students through the construction of a parallelogram, a rectangle, a square, and a rhombus. Students then

More information

*Students will answer the following warm-up questions: Name each of the following figures. Can each figure have more than one name? Why or why not?

*Students will answer the following warm-up questions: Name each of the following figures. Can each figure have more than one name? Why or why not? Student Lesson Plan Topic: Quadrilateral Properties and Relationships Subject Area/Content: General Education Geometry/Integrated II Course: 10 th Grade Time: 2-60 minute classes Lesson Objectives: 1.

More information

Featured Mathematical Practice: MP.5. Use appropriate tools strategically. MP.6. Attend to precision.

Featured Mathematical Practice: MP.5. Use appropriate tools strategically. MP.6. Attend to precision. Domain: Geometry 4.G Mathematical Content Standard: 1. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures.

More information

Wallingford Public Schools - HIGH SCHOOL COURSE OUTLINE

Wallingford Public Schools - HIGH SCHOOL COURSE OUTLINE Wallingford Public Schools - HIGH SCHOOL COURSE OUTLINE Course Title: Geometry Course Number: A 1223, G1224 Department: Mathematics Grade(s): 10-11 Level(s): Academic and General Objectives that have an

More information

2. If C is the midpoint of AB and B is the midpoint of AE, can you say that the measure of AC is 1/4 the measure of AE?

2. If C is the midpoint of AB and B is the midpoint of AE, can you say that the measure of AC is 1/4 the measure of AE? MATH 206 - Midterm Exam 2 Practice Exam Solutions 1. Show two rays in the same plane that intersect at more than one point. Rays AB and BA intersect at all points from A to B. 2. If C is the midpoint of

More information

GEOMETRY 101* EVERYTHING YOU NEED TO KNOW ABOUT GEOMETRY TO PASS THE GHSGT!

GEOMETRY 101* EVERYTHING YOU NEED TO KNOW ABOUT GEOMETRY TO PASS THE GHSGT! GEOMETRY 101* EVERYTHING YOU NEED TO KNOW ABOUT GEOMETRY TO PASS THE GHSGT! FINDING THE DISTANCE BETWEEN TWO POINTS DISTANCE FORMULA- (x₂-x₁)²+(y₂-y₁)² Find the distance between the points ( -3,2) and

More information

Maths Toolkit Teacher s notes

Maths Toolkit Teacher s notes Angles turtle Year 7 Identify parallel and perpendicular lines; know the sum of angles at a point, on a straight line and in a triangle; recognise vertically opposite angles. Use a ruler and protractor

More information

Carroll County Public Schools Elementary Mathematics Instructional Guide (5 th Grade) August-September (12 days) Unit #1 : Geometry

Carroll County Public Schools Elementary Mathematics Instructional Guide (5 th Grade) August-September (12 days) Unit #1 : Geometry Carroll County Public Schools Elementary Mathematics Instructional Guide (5 th Grade) Common Core and Research from the CCSS Progression Documents Geometry Students learn to analyze and relate categories

More information

22.1 Interior and Exterior Angles

22.1 Interior and Exterior Angles Name Class Date 22.1 Interior and Exterior ngles Essential Question: What can you say about the interior and exterior angles of a triangle and other polygons? Resource Locker Explore 1 Exploring Interior

More information

1. A person has 78 feet of fencing to make a rectangular garden. What dimensions will use all the fencing with the greatest area?

1. A person has 78 feet of fencing to make a rectangular garden. What dimensions will use all the fencing with the greatest area? 1. A person has 78 feet of fencing to make a rectangular garden. What dimensions will use all the fencing with the greatest area? (a) 20 ft x 19 ft (b) 21 ft x 18 ft (c) 22 ft x 17 ft 2. Which conditional

More information

Activity 5. Cross-Fencing Pastures. In this activity you will. Introduction. Investigation. Objective. Materials

Activity 5. Cross-Fencing Pastures. In this activity you will. Introduction. Investigation. Objective. Materials . Objective To use Geoboard to determine the area of shapes (polygons) by dissection Activity 5 Materials TI-73 Student Activity pages (pp. 54 59) Cross-Fencing Pastures In this activity you will Review

More information

CHAPTER 6. Polygons, Quadrilaterals, and Special Parallelograms

CHAPTER 6. Polygons, Quadrilaterals, and Special Parallelograms CHAPTER 6 Polygons, Quadrilaterals, and Special Parallelograms Table of Contents DAY 1: (Ch. 6-1) SWBAT: Find measures of interior and exterior angles of polygons Pgs: 1-7 HW: Pgs: 8-10 DAY 2: (6-2) Pgs:

More information

Geometry Course Summary Department: Math. Semester 1

Geometry Course Summary Department: Math. Semester 1 Geometry Course Summary Department: Math Semester 1 Learning Objective #1 Geometry Basics Targets to Meet Learning Objective #1 Use inductive reasoning to make conclusions about mathematical patterns Give

More information

Vocabulary List Geometry Altitude- the perpendicular distance from the vertex to the opposite side of the figure (base)

Vocabulary List Geometry Altitude- the perpendicular distance from the vertex to the opposite side of the figure (base) GEOMETRY Vocabulary List Geometry Altitude- the perpendicular distance from the vertex to the opposite side of the figure (base) Face- one of the polygons of a solid figure Diagonal- a line segment that

More information

Polygon Properties and Tiling

Polygon Properties and Tiling ! Polygon Properties and Tiling You learned about angles and angle measure in Investigations and 2. What you learned can help you figure out some useful properties of the angles of a polygon. Let s start

More information

1.1. Building Blocks of Geometry EXAMPLE. Solution a. P is the midpoint of both AB and CD. Q is the midpoint of GH. CONDENSED

1.1. Building Blocks of Geometry EXAMPLE. Solution a. P is the midpoint of both AB and CD. Q is the midpoint of GH. CONDENSED CONDENSED LESSON 1.1 Building Blocks of Geometry In this lesson you will Learn about points, lines, and planes and how to represent them Learn definitions of collinear, coplanar, line segment, congruent

More information

Conjectures. Chapter 2. Chapter 3

Conjectures. Chapter 2. Chapter 3 Conjectures Chapter 2 C-1 Linear Pair Conjecture If two angles form a linear pair, then the measures of the angles add up to 180. (Lesson 2.5) C-2 Vertical Angles Conjecture If two angles are vertical

More information

4 Mathematics Curriculum

4 Mathematics Curriculum Common Core 4 Mathematics Curriculum G R A D E GRADE 4 MODULE 4 Table of Contents GRADE 4 MODULE 4 Angle Measure and Plane Figures Module Overview... i Topic A: Lines and Angles... 4.A.1 Topic B: Angle

More information

Pre-Algebra IA Grade Level 8

Pre-Algebra IA Grade Level 8 Pre-Algebra IA Pre-Algebra IA introduces students to the following concepts and functions: number notation decimals operational symbols inverse operations of multiplication and division rules for solving

More information

Ch 3 Worksheets S15 KEY LEVEL 2 Name 3.1 Duplicating Segments and Angles [and Triangles]

Ch 3 Worksheets S15 KEY LEVEL 2 Name 3.1 Duplicating Segments and Angles [and Triangles] h 3 Worksheets S15 KEY LEVEL 2 Name 3.1 Duplicating Segments and ngles [and Triangles] Warm up: Directions: Draw the following as accurately as possible. Pay attention to any problems you may be having.

More information

6-1 Angles of Polygons

6-1 Angles of Polygons Find the sum of the measures of the interior angles of each convex polygon. 1. decagon A decagon has ten sides. Use the Polygon Interior Angles Sum Theorem to find the sum of its interior angle measures.

More information

Geometry Module 4 Unit 2 Practice Exam

Geometry Module 4 Unit 2 Practice Exam Name: Class: Date: ID: A Geometry Module 4 Unit 2 Practice Exam Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which diagram shows the most useful positioning

More information

Finding Parallelogram Vertices

Finding Parallelogram Vertices About Illustrations: Illustrations of the Standards for Mathematical Practice (SMP) consist of several pieces, including a mathematics task, student dialogue, mathematical overview, teacher reflection

More information

Geometry and Spatial Reasoning

Geometry and Spatial Reasoning Mathematics TEKS Refinement 2006 6-8 Tarleton State University Geometry and Spatial Reasoning Activity: TEKS: Creating Venn Diagrams with Quadrilaterals (6.6) Geometry and spatial reasoning. The student

More information

CHAPTER 10 GEOMETRY: ANGLES, TRIANGLES, AND DISTANCE (3 WEEKS)...

CHAPTER 10 GEOMETRY: ANGLES, TRIANGLES, AND DISTANCE (3 WEEKS)... Table of Contents CHAPTER 10 GEOMETRY: ANGLES, TRIANGLES, AND DISTANCE (3 WEEKS)... 10.0 ANCHOR PROBLEM: REASONING WITH ANGLES OF A TRIANGLE AND RECTANGLES... 6 10.1 ANGLES AND TRIANGLES... 7 10.1a Class

More information