# Lesson 7: Drawing Parallelograms

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Student Outcomes Students use a protractor, ruler, and setsquare to draw parallelograms based on given conditions. Lesson Notes In Lesson 6, students drew a series of figures (e.g., complementary angles, vertical angles, circles of different radii, and isosceles triangles). In Lesson 7, students become familiar with a geometry tool known as the setsquare and use it to draw parallelograms under a variety of conditions. Similar to the previous lesson, students should have experience using tools and experience making comparisons between drawings done with tools and drawings done freehand. Work in this lesson embodies Mathematical Practice 5. Classwork Opening (5 minutes) A setsquare is a triangle with a right angle. It can be made out of plastic or out of paper. Have students create their own setsquares out of paper or cardstock. Place tape on the edges of your setsquare. Have students use a setsquare and a ruler to check if lines are parallel. Date: 4/9/14 73

2 We want to determine whether these lines are parallel. Identify the two sides of the setsquare that meet at the right angle as shown, and. Place the ruler against and align with one of the two lines. Notice that the ruler must be perpendicular to line. Slide the setsquare along the ruler. Try to line up with the other line. If the edge of the setsquare aligns with the line, the two lines are parallel. If the edge of the setsquare does not align with the line, then the two lines are not parallel. Have students use a setsquare and ruler to draw a line parallel to through the point. We want to draw a line through parallel to. Align with. Slide the setsquare along the ruler until it is possible to draw a segment through along. Use your ruler to extend the segment through. The two lines are parallel. Date: 4/9/14 74

3 Example 1 (5 minutes) Example 1 Use what you know about drawing parallel lines with a setsquare to draw rectangle with dimensions of your choice. State the steps you used to draw your rectangle, and compare those steps to those of a partner s. Scaffolding: Possible steps: Draw first. Align the setsquare so that one leg aligns with and place the ruler against the other leg of the setsquare; mark a point, cm away from. Draw a line parallel to through. Realign the setsquare with and situate the ruler so that it passes through and draw with a length of cm. is now drawn perpendicular to. Mark the intersection of the line through and the parallel line to as. Repeat the steps to determine. Consider providing a visual reminder (e.g., a chart handout or poster) naming the quadrilaterals and their key properties. Example 2 (7 minutes) Example 2 Use what you know about drawing parallel lines with a setsquare to draw rectangle with cm and cm. Write a plan for the steps you will take to draw. Draw first. Align the setsquare so that one leg aligns with and place the ruler against the other leg of the setsquare; mark a point, cm away from. Draw a line parallel to through. To create the right angle at, align the setsquare so that the leg of the setsquare aligns with and situate the ruler so that the outer edge of the ruler passes through and draw a line through. Mark the intersection of the line through and the parallel line to as. Repeat the steps to determine. Make sure that students label all vertices, right angles and measurements. This example also provides an opportunity to review the definition of diagonal: In a quadrilateral, the segments and would be called the diagonals of the quadrilateral. With respect to the solution, students will not respond (and are not expected to respond) with the level of detail found in the solution. The goal is to get them thinking about how they will use their newly acquired skills to draw a rectangle with the setsquare. Share the solution so they have exposure to the precision needed for clear instructions. Eventually, in Grade 10, students will write instructions so precise that a person who doesn t know what a rectangle is would still be able to draw one by using the instructions. Example 3 (7 minutes) Example 3 Use a setsquare, ruler and protractor to draw parallelogram so that the measurement of, cm, the measurement of, and the altitude to is cm. Steps to draw the figure: Draw first. Align the setsquare and ruler so one leg of the setsquare aligns with and mark a point, cm from. Slide the setsquare along the ruler so that one side of the setsquare passes through and draw a line through ; this line is parallel to. Using as one ray of, draw so that the measurement of and that the ray intersects with the line parallel to (the intersection is ). Draw so that the measurement of ; the ray should be drawn to intersect with the line parallel to (the intersection is ). Date: 4/9/14 75

4 Exercise 1 (6 minutes) Exercise 1 Use a setsquare, ruler, and protractor to draw parallelogram so that the measurement of, cm, the measurement of, and the altitude to is cm. Steps to draw the figure: Draw first. Align the setsquare and ruler so one leg of the setsquare aligns with and mark a point, cm from. Slide the setsquare along the ruler so that one side of the setsquare passes through and draw a line through ; this line is parallel to. Using as one ray of, draw so that the measurement of and that the ray intersects with the line parallel to (the intersection is ). Draw so that the measurement of ; the ray should be drawn to intersect with the line parallel to (the intersection is ). Example 4 (7 minutes) Example 4 Use a setsquare, ruler and protractor to draw rhombus so that the measurement of, the measurement of, and each side of the rhombus measures cm. Steps to draw the figure: Draw first. Using as one ray of, draw so that the measurement of. The other ray, or the to-be side of the rhombus,, should be cm in length; label the endpoint of the segment as. Align the setsquare and ruler so one leg of the setsquare aligns with and the edge of the ruler passes through. Slide the setsquare along the ruler so that the edge of the setsquare passes through and draw a line along the edge of the setsquare. This line is parallel to. Now align the setsquare and ruler so one leg of the setsquare aligns with and the edge of the ruler passes through. Slide the setsquare along the ruler so that the edge of the setsquare passes through and draw a line along the edge of the setsquare. This line is parallel to. Along this line, measure a segment cm with as one endpoint, and label the other endpoint. Join to. Closing (1 minute) Why are setsquares useful in drawing parallelograms? They give us a means to draw parallel lines for the sides of parallelograms. Exit Ticket (6 minutes) Date: 4/9/14 76

5 Name Date Exit Ticket Use what you know about drawing parallel lines with a setsquare to draw square with cm. Explain how you created your drawing. Date: 4/9/14 77

6 Exit Ticket Sample Solutions Use what you know about drawing parallel lines with a setsquare to draw square with cm. Explain how you created your drawing. Draw (any side will do here) first. Align the setsquare and ruler so that one leg of the setsquare aligns with ; mark a point, cm away from. Draw a line parallel to through. To create the right angle at, align the setsquare so that the leg of the setsquare aligns with and situate the ruler so that the outer edge of the ruler passes through and draw a line through. Mark the intersection of the line through and the parallel line to as ; join and. Repeat the steps to determine and join and. Problem Set Sample Solutions 1. Draw rectangle with cm and cm. Steps to draw the figure: Draw first. Align the setsquare so that one leg aligns with and place the ruler against the other leg of the setsquare; mark a point,, cm away from. Draw a line parallel to through. To create the right angle at, align the setsquare so that its leg aligns with and situate the ruler so that the outer edge of the ruler passes through and draw a line through. Mark the intersection of the line through and the parallel line to as. Repeat the steps to determine. 2. Use a setsquare, ruler and protractor to draw parallelogram so that the measurement of, cm,, and the altitude to is cm Steps to draw the figure: Draw first. Align the setsquare and ruler so one leg of the setsquare aligns with and mark a point,, cm from. Slide the setsquare along the ruler so that one side of the setsquare passes through and draw a line through ; this line is parallel to. Using as one ray of, draw so that the measurement of and that the ray intersects with the line parallel to (the intersection is ). Draw so that the measurement of ; the ray should be drawn to intersect with the line parallel to (the intersection is ). 3. Use a setsquare, ruler and protractor to draw rhombus so that the measurement of, and each side of the rhombus measures cm. Steps to draw the figure: Draw first. Using as one ray of, draw so that the measurement of. The other ray, or to-be side of the rhombus,, should be cm in length; label the endpoint of the segment as. Align the setsquare and ruler so one leg of the setsquare aligns with and the edge of the ruler passes through. Slide the setsquare along the ruler so that the edge of the setsquare passes through and draw a line along the edge of the setsquare. This line is parallel to. Now align the setsquare and ruler so one leg of the setsquare aligns with and the edge of the ruler passes through. Slide the setsquare along the ruler so that the edge of the setsquare passes through and draw a line along the edge of the setsquare. This line is parallel to. Along this line, measure a segment cm with as one endpoint, and label the other endpoint. Join to. Date: 4/9/14 78

7 altitude,to,ab NYS COMMON CORE MATHEMATICS CURRICULUM Lesson The following table contains partial information for a parallelogram. Using no tools, make a sketch of the parallelogram. Then use a ruler, protractor, and setsquare to draw an accurate picture. D C D C altitude,to,bc A B A B Altitude to Altitude to 4. cm cm cm cm 5. cm cm cm cm 6. cm cm cm cm 7. Use what you know about drawing parallel lines with a setsquare to draw trapezoid with parallel sides and. The length of is cm and the length of cm; the height between the parallel sides is cm. Write a plan for the steps you will take to draw. Draw (or ) first. Align the setsquare and ruler so that one leg of the setsquare aligns with ; mark a point, cm away from. Draw a line parallel to through. Once a line parallel to has been drawn through, measure a portion of the line to be cm and label either endpoint as and. Join to and to. 8. Draw rectangle with cm and cm using appropriate tools. Draw first. Align the setsquare so that one leg aligns with and place the ruler against the other leg of the setsquare; mark a point,, cm away from. Draw a line parallel to through. To create the right angle at, align the setsquare so that its leg aligns with and situate the ruler so that its outer edge passes through, and then draw a line through. Mark the intersection of the line through and the parallel line to as. Repeat the steps to determine. 9. Challenge: Determine the area of the largest rectangle that will fit inside an equilateral triangle with side length cm Students will quickly discover that rectangles of different dimensions can be drawn; finding the largest rectangle may take multiple efforts. The maximum possible area is cm 2. Date: 4/9/14 79

8 Supplement fold Date: 4/9/14 80

### Lesson 6: Drawing Geometric Shapes

Student Outcomes Students use a compass, protractor, and ruler to draw geometric shapes based on given conditions. Lesson Notes The following sequence of lessons is based on standard 7.G.A.2: Draw (freehand,

### 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

### *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

### 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.

### 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

### 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

### 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

### 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

### 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

### 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.

### 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,

### 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

### Unit Background. Stage 1: Big Goals

Course: 7 th Grade Mathematics Unit Background Unit Title Angle Relationships, Transversals & 3-Dimensional Geometry Does the unit title reflect the standards? PCCMS Unit Reviewer (s): Unit Designer: Resources

### 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

### 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

### 2006 Geometry Form A Page 1

2006 Geometry Form Page 1 1. he hypotenuse of a right triangle is 12" long, and one of the acute angles measures 30 degrees. he length of the shorter leg must be: () 4 3 inches () 6 3 inches () 5 inches

### 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.

### 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

### 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

### **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:

### Objectives. Cabri Jr. Tools

Activity 24 Angle Bisectors and Medians of Quadrilaterals Objectives To investigate the properties of quadrilaterals formed by angle bisectors of a given quadrilateral To investigate the properties of

### Lesson 18: Determining Surface Area of Three Dimensional Figures

Lesson 18: Determining the Surface Area of Three Dimensional Figures Student Outcomes Students determine that a right rectangular prism has six faces: top and bottom, front and back, and two sides. They

### Identify relationships between and among linear and square metric units. area = length x width = 60 cm x 25 cm = 1500 cm 2

1 Unit Relationships Identify relationships between and among linear and square metric units. 1. Express each area in square centimetres. a) 8 m 2 80 000 cm 2 c) 3.5 m 2 35 000 cm 2 b) 12 m 2 120 000 cm

### A = ½ x b x h or ½bh or bh. Formula Key A 2 + B 2 = C 2. Pythagorean Theorem. Perimeter. b or (b 1 / b 2 for a trapezoid) height

Formula Key b 1 base height rea b or (b 1 / b for a trapezoid) h b Perimeter diagonal P d (d 1 / d for a kite) d 1 d Perpendicular two lines form a angle. Perimeter P = total of all sides (side + side

### *1. Understand the concept of a constant number like pi. Know the formula for the circumference and area of a circle.

Students: 1. Students deepen their understanding of measurement of plane and solid shapes and use this understanding to solve problems. *1. Understand the concept of a constant number like pi. Know the

### 2. The scale factor for a dilation where a point is pulled towards the center must be < r <.

im #2: How do we create scale drawings using the ratio method? o Now: Geometry H 1. Figure I has been dilated to create figure II. What conclusion can you make about the numerical value of the scale factor?

### Line AB (no Endpoints) Ray with Endpoint A. Line Segments with Endpoints A and B. Angle is formed by TWO Rays with a common Endpoint.

Section 8 1 Lines and Angles Point is a specific location in space.. Line is a straight path (infinite number of points). Line Segment is part of a line between TWO points. Ray is part of the line that

### 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 &

### 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

### Lesson 3.1 Duplicating Segments and Angles

Lesson 3.1 Duplicating Segments and ngles In Exercises 1 3, use the segments and angles below. Q R S 1. Using only a compass and straightedge, duplicate each segment and angle. There is an arc in each

### 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

### 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

### 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

### 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

### 1) Perpendicular bisector 2) Angle bisector of a line segment

1) Perpendicular bisector 2) ngle bisector of a line segment 3) line parallel to a given line through a point not on the line by copying a corresponding angle. 1 line perpendicular to a given line through

### 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

### 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

### Algebra Geometry Glossary. 90 angle

lgebra Geometry Glossary 1) acute angle an angle less than 90 acute angle 90 angle 2) acute triangle a triangle where all angles are less than 90 3) adjacent angles angles that share a common leg Example:

### (a) 5 square units. (b) 12 square units. (c) 5 3 square units. 3 square units. (d) 6. (e) 16 square units

1. Find the area of parallelogram ACD shown below if the measures of segments A, C, and DE are 6 units, 2 units, and 1 unit respectively and AED is a right angle. (a) 5 square units (b) 12 square units

### 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

### 10.1: Areas of Parallelograms and Triangles

10.1: Areas of Parallelograms and Triangles Important Vocabulary: By the end of this lesson, you should be able to define these terms: Base of a Parallelogram, Altitude of a Parallelogram, Height of a

### How does one make and support a reasonable conclusion regarding a problem? How does what I measure influence how I measure?

Middletown Public Schools Mathematics Unit Planning Organizer Subject Mathematics Grade/Course Grade 7 Unit 3 Two and Three Dimensional Geometry Duration 23 instructional days (+4 days reteaching/enrichment)

### 7. 6 Justifying Constructions

31 7. 6 Justifying Constructions A Solidify Understanding Task CC BY THOR https://flic.kr/p/9qkxv Compass and straightedge constructions can be justified using such tools as: the definitions and properties

Dear Grade 4 Families, During the next few weeks, our class will be exploring geometry. Through daily activities, we will explore the relationship between flat, two-dimensional figures and solid, three-dimensional

### Objective. Materials. Find the areas of parallelograms and trapezoids. Discover shortcut ways of finding the areas of parallelograms and trapezoids.

. Objective To use Geoboard to determine the areas of quadrilaterals between parallel lines Activity 4 Materials TI-73 Student Activity pages (pp. 41 45) Slide Along In this activity you will Find the

### 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

### Isosceles triangles. Key Words: Isosceles triangle, midpoint, median, angle bisectors, perpendicular bisectors

Isosceles triangles Lesson Summary: Students will investigate the properties of isosceles triangles. Angle bisectors, perpendicular bisectors, midpoints, and medians are also examined in this lesson. A

### Area. Area Overview. Define: Area:

Define: Area: Area Overview Kite: Parallelogram: Rectangle: Rhombus: Square: Trapezoid: Postulates/Theorems: Every closed region has an area. If closed figures are congruent, then their areas are equal.

### 39 Symmetry of Plane Figures

39 Symmetry of Plane Figures In this section, we are interested in the symmetric properties of plane figures. By a symmetry of a plane figure we mean a motion of the plane that moves the figure so that

### Unknown Angle Problems with Inscribed Angles in Circles

: Unknown Angle Problems with Inscribed Angles in Circles Student Outcomes Use the inscribed angle theorem to find the measures of unknown angles. Prove relationships between inscribed angles and central

### 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

### Inscribed Angle Theorem and Its Applications

: Student Outcomes Prove the inscribed angle theorem: The measure of a central angle is twice the measure of any inscribed angle that intercepts the same arc as the central angle. Recognize and use different

### Teaching Guidelines. Knowledge and Skills: Can specify defining characteristics of common polygons

CIRCLE FOLDING Teaching Guidelines Subject: Mathematics Topics: Geometry (Circles, Polygons) Grades: 4-6 Concepts: Property Diameter Radius Chord Perimeter Area Knowledge and Skills: Can specify defining

### 1. Find the length of BC in the following triangles. It will help to first find the length of the segment marked X.

1 Find the length of BC in the following triangles It will help to first find the length of the segment marked X a: b: Given: the diagonals of parallelogram ABCD meet at point O The altitude OE divides

### *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.

### Lines, Segments, Rays, and Angles

Line and Angle Review Thursday, July 11, 2013 10:22 PM Lines, Segments, Rays, and Angles Slide Notes Title Lines, Segment, Ray A line goes on forever, so we use an arrow on each side to indicate that.

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

### 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

### Centroid: The point of intersection of the three medians of a triangle. Centroid

Vocabulary Words Acute Triangles: A triangle with all acute angles. Examples 80 50 50 Angle: A figure formed by two noncollinear rays that have a common endpoint and are not opposite rays. Angle Bisector:

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2009 8:30 to 11:30 a.m., only.

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 13, 2009 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of your

### 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

### Content Area: GEOMETRY Grade 9 th Quarter 1 st Curso Serie Unidade

Content Area: GEOMETRY Grade 9 th Quarter 1 st Curso Serie Unidade Standards/Content Padrões / Conteúdo Learning Objectives Objetivos de Aprendizado Vocabulary Vocabulário Assessments Avaliações Resources

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

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

### PERIMETER AND AREA. In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures.

PERIMETER AND AREA In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures. Perimeter Perimeter The perimeter of a polygon, denoted by P, is the

### 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

### Formula for the Area of a Triangle Objective To guide the development and use of a formula for the area of a triangle.

Formula for the rea of a Triangle Objective To guide the development and use of a formula for the area of a triangle. www.everydaymathonline.com epresentations etoolkit lgorithms Practice EM Facts Workshop

### 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

### 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

### GEOMETRY. Constructions OBJECTIVE #: G.CO.12

GEOMETRY Constructions OBJECTIVE #: G.CO.12 OBJECTIVE Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic

### Lesson 2: Circles, Chords, Diameters, and Their Relationships

Circles, Chords, Diameters, and Their Relationships Student Outcomes Identify the relationships between the diameters of a circle and other chords of the circle. Lesson Notes Students are asked to construct

### Family Letters. Assessment Management. Playing Fraction Of

Formula for the Area of a Parallelogram Objectives To review the properties of parallelograms; and to guide the development and use of a formula for the area of a parallelogram. www.everydaymathonline.com

### Arc Length and Areas of Sectors

Student Outcomes When students are provided with the angle measure of the arc and the length of the radius of the circle, they understand how to determine the length of an arc and the area of a sector.

### G6-9 Area of Composite Shapes

G6-9 Area of Composite Shapes 1. a) Calculate the area of each figure. b) Draw a line to show how Shape C can be divided into rectangles A and. i) ii) A C A C Area of A = Area of A = Area of = Area of

### Special case: Square. The same formula works, but you can also use A= Side x Side or A= (Side) 2

Geometry Chapter 11/12 Review Shape: Rectangle Formula A= Base x Height Special case: Square. The same formula works, but you can also use A= Side x Side or A= (Side) 2 Height = 6 Base = 8 Area = 8 x 6

### 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

### 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,

### Sec 1.1 CC Geometry - Constructions Name: 1. [COPY SEGMENT] Construct a segment with an endpoint of C and congruent to the segment AB.

Sec 1.1 CC Geometry - Constructions Name: 1. [COPY SEGMENT] Construct a segment with an endpoint of C and congruent to the segment AB. A B C **Using a ruler measure the two lengths to make sure they have

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, August 18, 2010 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of

### CSU Fresno Problem Solving Session. Geometry, 17 March 2012

CSU Fresno Problem Solving Session Problem Solving Sessions website: http://zimmer.csufresno.edu/ mnogin/mfd-prep.html Math Field Day date: Saturday, April 21, 2012 Math Field Day website: http://www.csufresno.edu/math/news

### Lines That Pass Through Regions

: Student Outcomes Given two points in the coordinate plane and a rectangular or triangular region, students determine whether the line through those points meets the region, and if it does, they describe

### Perimeter and area formulas for common geometric figures:

Lesson 10.1 10.: Perimeter and Area of Common Geometric Figures Focused Learning Target: I will be able to Solve problems involving perimeter and area of common geometric figures. Compute areas of rectangles,

### Constructing Perpendicular Bisectors

Page 1 of 5 L E S S O N 3.2 To be successful, the first thing to do is to fall in love with your work. SISTER MARY LAURETTA Constructing Perpendicular Bisectors Each segment has exactly one midpoint. A

### SGS4.3 Stage 4 Space & Geometry Part A Activity 2-4

SGS4.3 Stage 4 Space & Geometry Part A Activity 2-4 Exploring triangles Resources required: Each pair students will need: 1 container (eg. a rectangular plastic takeaway container) 5 long pipe cleaners

### 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

### GEOMETRY FINAL EXAM REVIEW

GEOMETRY FINL EXM REVIEW I. MTHING reflexive. a(b + c) = ab + ac transitive. If a = b & b = c, then a = c. symmetric. If lies between and, then + =. substitution. If a = b, then b = a. distributive E.

### 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

### Classifying Lesson 1 Triangles

Classifying Lesson 1 acute angle congruent scalene Classifying VOCABULARY right angle isosceles Venn diagram obtuse angle equilateral You classify many things around you. For example, you might choose

### Algebra III. Lesson 33. Quadrilaterals Properties of Parallelograms Types of Parallelograms Conditions for Parallelograms - Trapezoids

Algebra III Lesson 33 Quadrilaterals Properties of Parallelograms Types of Parallelograms Conditions for Parallelograms - Trapezoids Quadrilaterals What is a quadrilateral? Quad means? 4 Lateral means?

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, June 17, 2010 1:15 to 4:15 p.m., only Student Name: School Name: Print your name and the name of your

### 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

### The Inscribed Angle Alternate A Tangent Angle

Student Outcomes Students use the inscribed angle theorem to prove other theorems in its family (different angle and arc configurations and an arc intercepted by an angle at least one of whose rays is

### 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

### CLASSIFYING GEOMETRIC SHAPES

4 CLASSIFYING GEOMETRIC SHAPES INSTRUCTIONAL ACTIVITY Lesson 2 LEARNING GOAL Students will classify shapes according to single attributes. PRIMARY ACTIVITY Students will create groups of shapes that have

### Final Review Problems Geometry AC Name

Final Review Problems Geometry Name SI GEOMETRY N TRINGLES 1. The measure of the angles of a triangle are x, 2x+6 and 3x-6. Find the measure of the angles. State the theorem(s) that support your equation.

### Math Common Core Standards Fourth Grade

Operations and Algebraic Thinking (OA) Use the four operations with whole numbers to solve problems. OA.4.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 7 as a statement

### Unit 8 Angles, 2D and 3D shapes, perimeter and area

Unit 8 Angles, 2D and 3D shapes, perimeter and area Five daily lessons Year 6 Spring term Recognise and estimate angles. Use a protractor to measure and draw acute and obtuse angles to Page 111 the nearest

### 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

### The formula for the area of a parallelogram is: A = bh, where b is the length of the base and h is the length of the height.

The formula for the area of a parallelogram is: A = h, where is the length of the ase and h is the length of the height. The formula for the area of a parallelogram is: A = h, where is the length of the