61 Properties and Attributes of Polygons


 Hester Blake
 2 years ago
 Views:
Transcription
1 61 Properties and Attributes of Polygons Warm Up Lesson Presentation Lesson Quiz Geometry
2 Warm Up 1. A? is a threesided polygon. triangle 2. A? is a foursided polygon. quadrilateral Evaluate each expression for n = (n 4) (n 3) Solve for a a + 4a + 9a = 100 4
3 Objectives Classify polygons based on their sides and angles. Find and use the measures of interior and exterior angles of polygons.
4 side of a polygon vertex of a polygon diagonal regular polygon concave convex Vocabulary
5 In Lesson 24, you learned the definition of a polygon. Now you will learn about the parts of a polygon and about ways to classify polygons.
6 Each segment that forms a polygon is a side of the polygon. The common endpoint of two sides is a vertex of the polygon. A segment that connects any two nonconsecutive vertices is a diagonal.
7 You can name a polygon by the number of its sides. The table shows the names of some common polygons.
8 Remember! A polygon is a closed plane figure formed by three or more segments that intersect only at their endpoints.
9 Example 1A: Identifying Polygons Tell whether the figure is a polygon. If it is a polygon, name it by the number of sides. polygon, hexagon
10 Example 1B: Identifying Polygons Tell whether the figure is a polygon. If it is a polygon, name it by the number of sides. polygon, heptagon
11 Example 1C: Identifying Polygons Tell whether the figure is a polygon. If it is a polygon, name it by the number of sides. not a polygon
12 Check It Out! Example 1a Tell whether each figure is a polygon. If it is a polygon, name it by the number of its sides. not a polygon
13 Check It Out! Example 1b Tell whether the figure is a polygon. If it is a polygon, name it by the number of its sides. polygon, nonagon
14 Check It Out! Example 1c Tell whether the figure is a polygon. If it is a polygon, name it by the number of its sides. not a polygon
15 All the sides are congruent in an equilateral polygon. All the angles are congruent in an equiangular polygon. A regular polygon is one that is both equilateral and equiangular. If a polygon is not regular, it is called irregular.
16 A polygon is concave if any part of a diagonal contains points in the exterior of the polygon. If no diagonal contains points in the exterior, then the polygon is convex. A regular polygon is always convex.
17 Example 2A: Classifying Polygons Tell whether the polygon is regular or irregular. Tell whether it is concave or convex. irregular, convex
18 Example 2B: Classifying Polygons Tell whether the polygon is regular or irregular. Tell whether it is concave or convex. irregular, concave
19 Example 2C: Classifying Polygons Tell whether the polygon is regular or irregular. Tell whether it is concave or convex. regular, convex
20 Check It Out! Example 2a Tell whether the polygon is regular or irregular. Tell whether it is concave or convex. regular, convex
21 Check It Out! Example 2b Tell whether the polygon is regular or irregular. Tell whether it is concave or convex. irregular, concave
22 To find the sum of the interior angle measures of a convex polygon, draw all possible diagonals from one vertex of the polygon. This creates a set of triangles. The sum of the angle measures of all the triangles equals the sum of the angle measures of the polygon.
23 Remember! By the Triangle Sum Theorem, the sum of the interior angle measures of a triangle is 180.
24
25 In each convex polygon, the number of triangles formed is two less than the number of sides n. So the sum of the angle measures of all these triangles is (n 2)180.
26 Example 3A: Finding Interior Angle Measures and Sums in Polygons Find the sum of the interior angle measures of a convex heptagon. (n 2)180 (7 2) Polygon Sum Thm. A heptagon has 7 sides, so substitute 7 for n. Simplify.
27 Example 3B: Finding Interior Angle Measures and Sums in Polygons Find the measure of each interior angle of a regular 16gon. Step 1 Find the sum of the interior angle measures. (n 2)180 (16 2)180 = 2520 Polygon Sum Thm. Substitute 16 for n and simplify. Step 2 Find the measure of one interior angle. The int. s are, so divide by 16.
28 Example 3C: Finding Interior Angle Measures and Sums in Polygons Find the measure of each interior angle of pentagon ABCDE. (5 2)180 = 540 Polygon Sum Thm. m A + m B + m C + m D + m E = 540 Polygon Sum Thm. 35c + 18c + 32c + 32c + 18c = c = 540 Combine like terms. c = 4 Divide both sides by 135. Substitute.
29 Example 3C Continued m A = 35(4 ) = 140 m B = m E = 18(4 ) = 72 m C = m D = 32(4 ) = 128
30 Check It Out! Example 3a Find the sum of the interior angle measures of a convex 15gon. (n 2)180 (15 2) Polygon Sum Thm. A 15gon has 15 sides, so substitute 15 for n. Simplify.
31 Find the measure of each interior angle of a regular decagon. Step 1 Find the sum of the interior angle measures. (n 2)180 Check It Out! Example 3b (10 2)180 = 1440 Polygon Sum Thm. Substitute 10 for n and simplify. Step 2 Find the measure of one interior angle. The int. s are, so divide by 10.
32 In the polygons below, an exterior angle has been measured at each vertex. Notice that in each case, the sum of the exterior angle measures is 360.
33 Remember! An exterior angle is formed by one side of a polygon and the extension of a consecutive side.
34
35 Example 4A: Finding Interior Angle Measures and Sums in Polygons Find the measure of each exterior angle of a regular 20gon. A 20gon has 20 sides and 20 vertices. sum of ext. s = 360. Polygon Sum Thm. measure of one ext. = A regular 20gon has 20 ext. s, so divide the sum by 20. The measure of each exterior angle of a regular 20gon is 18.
36 Example 4B: Finding Interior Angle Measures and Sums in Polygons Find the value of b in polygon FGHJKL. Polygon Ext. Sum Thm. 15b + 18b + 33b + 16b + 10b + 28b = b = 360 Combine like terms. b = 3 Divide both sides by 120.
37 Check It Out! Example 4a Find the measure of each exterior angle of a regular dodecagon. A dodecagon has 12 sides and 12 vertices. sum of ext. s = 360. Polygon Sum Thm. measure of one ext. A regular dodecagon has 12 ext. s, so divide the sum by 12. The measure of each exterior angle of a regular dodecagon is 30.
38 Check It Out! Example 4b Find the value of r in polygon JKLM. 4r + 7r + 5r + 8r = 360 Polygon Ext. Sum Thm. 24r = 360 Combine like terms. r = 15 Divide both sides by 24.
TEKS: G2B, G3B, G4A, G5A, G5B, G9B The student will determine the validity of conjectures. The student will construct and justify statements.
TEKS: G2B, G3B, G4A, G5A, G5B, G9B The student will determine the validity of conjectures. The student will construct and justify statements. The student will select an appropriate representation to solve
More informationNovember 11, Polygons. poly means "many" gon means "angles" polygon means "many angles"
3.5 Polygons poly means "many" gon means "angles" polygon means "many angles" note that each polygon is formed by coplanar segments (called sides) such that: each segment intersects exactly 2 other segments,
More informationPolygons 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 information7.3 & 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 informationUnit 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 informationA 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 informationGeometry. 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 informationUnit 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 informationSum of the interior angles of a (n  2)180 polygon ~, Sum of the exterior angles of a 360 polygon
Name Geometry Polygons Sum of the interior angles of a (n  2)180 polygon ~, Sum of the exterior angles of a 360 polygon Each interior angle of a regular (n  2)180 i polygon n Each exterior angle of a
More informationA of a polygon is a segment that joins two nonconsecutive vertices. 1. How many degrees are in a triangle?
8.1 Find Angle Measures in Polygons SWBAT: find interior and exterior angle measures in polygons. Common Core: G.CO.11, G.CO.13, G.SRT.5 Do Now Fill in the blank. A of a polygon is a segment that joins
More informationGeometry. 1.4 Perimeter and Area in the Coordinate Plane
Geometry 1.4 Perimeter and Area in the Coordinate Plane Essential Question How can I find the perimeter and area of a polygon in a coordinate plane? What You Will Learn Classify polygons Find perimeters
More informationCHAPTER 6. Polygons, Quadrilaterals, and Special Parallelograms
CHAPTER 6 Polygons, Quadrilaterals, and Special Parallelograms Table of Contents DAY 1: (Ch. 61) SWBAT: Find measures of interior and exterior angles of polygons Pgs: 17 HW: Pgs: 810 DAY 2: (62) Pgs:
More informationPOLYGONS
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, twodimensional figure made of three or more nonintersecting straight
More informationUnit 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 information11.3 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 informationThe 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 informationLesson 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 informationHonors Packet on. Polygons, Quadrilaterals, and Special Parallelograms
Honors Packet on Polygons, Quadrilaterals, and Special Parallelograms Table of Contents DAY 1: (Ch. 61) SWBAT: Find measures of interior and exterior angles of polygons Pgs: #1 6 in packet HW: Pages 386
More informationChapter 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 information1 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 information115 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 informationPage How many sides does an octagon have? a) 4 b) 5 c) 6 d) 8 e) A regular hexagon has lines of symmetry. a) 2 b) 3 c) 4 d) 5 e) 6 1 9
Acc. Geometery Name Polygon Review Per/Sec. Date Determine whether each of the following statements is always, sometimes, or never true. 1. A regular polygon is convex. 2. Two sides of a polygon are noncollinear.
More informationThe Polygon AngleSum Theorems
61 The Polygon AngleSum Theorems Common Core State Standards GSRT.B.5 Use congruence... criteria to solve problems and prove relationships in geometric figures. MP 1, MP 3 Objectives To find the sum
More informationTopic : Exterior Angles  Worksheet How many degrees are there in the sum of the exterior angles of a regular hexagon?
Topic : Exterior Angles  Worksheet 1 regular hexagon? polygon having 20 3. If each polygon contains 40 O how many each polygon having 16 angle of a regular polygon having 8 a 5 sided polygon? polygon
More informationFind the sum of the measures of the interior angles of a polygon. Find the sum of the measures of the exterior angles of a polygon.
ngles of Polygons Find the sum of the measures of the interior angles of a polygon. Find the sum of the measures of the exterior angles of a polygon. Vocabulary diagonal does a scallop shell illustrate
More information61 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 information15 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 information8.1 Find Angle Measures in Polygons
8.1 Find Angle Measures in Polygons Obj.: To find angle measures in polygons. Key Vocabulary Diagonal  A diagonal of a polygon is a segment that joins two nonconsecutive vertices. Polygon ABCDE has two
More informationFiveMinute Check (over Lesson 1 5) CCSS Then/Now New Vocabulary Key Concepts: Polygons Example 1: Name and Classify Polygons Key Concepts:
FiveMinute Check (over Lesson 1 5) CCSS Then/Now New Vocabulary Key Concepts: Polygons Example 1: Name and Classify Polygons Key Concepts: Perimeter, Circumference, and Area Example 2: Find Perimeter
More informationTarget To know the properties of a rectangle
Target To know the properties of a rectangle (1) A rectangle is a 3D 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 informationPolygon 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 informationA segment that joins two nonconsecutive vertices of a polygon is called a diagonal. Polygon PQRST has two diagonals from vertex R, RP &* and RT&*.
age of 6 6. olygons Goal Identify and classify polygons. Find angle measures of quadrilaterals. Each traffic sign below is an example of a polygon. Notice that each sign is formed with straight lines.
More informationName: 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 informationExterior Angles of Polygons
easures, hape & pace EXEMPLAR 14: Exterior Angles of Polygons Objective: To explore the angle sum of the exterior angles of polygons Key Stage: 3 Learning Unit: Angle related with Lines and Rectilinear
More informationSHOW YOUR WORK CHECK YOUR WORK VALIDATE YOUR WORK! Unit 6: POLYGONS. Are these polygons? Justify your answer by explaining WHY or WHY NOT???
Unit 6: POLYGONS Are these polygons? Justify your answer by explaining WHY or WHY NOT??? a) b) c) Yes or No Why/Why not? Yes or No Why/Why not? Yes or No Why/Why not? a) What is a CONCAVE polygon? Use
More informationUNIT 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 informationActivity 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(n = # of sides) One interior angle:
6.1 What is a Polygon? Regular Polygon Polygon Formulas: (n = # of sides) One interior angle: 180(n 2) n Sum of the interior angles of a polygon = 180 (n  2) Sum of the exterior angles of a polygon =
More information10.1: 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
More informationVertex : is the point at which two sides of a polygon meet.
POLYGONS A polygon is a closed plane figure made up of several line segments that are joined together. The sides do not cross one another. Exactly two sides meet at every vertex. Vertex : is the point
More informationUnit 8 Geometry QUADRILATERALS. NAME Period
Unit 8 Geometry QUADRILATERALS NAME Period 1 A little background Polygon is the generic term for a closed figure with any number of sides. Depending on the number, the first part of the word Poly is replaced
More informationYear 10 Term 1 Homework
Yimin Math Centre Year 10 Term 1 Homework Student Name: Grade: Date: Score: Table of contents 10 Year 10 Term 1 Week 10 Homework 1 10.1 Deductive geometry.................................... 1 10.1.1 Basic
More information56 questions (multiple choice, check all that apply, and fill in the blank) The exam is worth 224 points.
6.1.1 Review: Semester Review Study Sheet Geometry Core Sem 2 (S2495808) Semester Exam Preparation Look back at the unit quizzes and diagnostics. Use the unit quizzes and diagnostics to determine which
More informationP o l y g o n s & A n g l e s POLYGONS & ANGLES.
P o l y g o n s & A n g l e s POLYGONS & ANGLES www.mathletics.com.au Polygons POLYGONS & Angles & ANGLES A shape which has straight sides only (no curved sides) is called a Polygon. The angles inside
More informationGeometry 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 informationGeometry. 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 informationCLASSIFIED NOMENCLATURE: THE FORMATION OF REGIONS  SIMPLE CLOSED CURVE FIGURES AND POLYGONS
CLASSIFIED NOMENCLATURE: THE FORMATION OF REGIONS  SIMPLE CLOSED CURVE FIGURES AND POLYGONS Material: Geometry Stick Box and Board A piece of string Paper and scissors Paper labels and pencil Presentation:
More informationGrade 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 informationTons of Free Math Worksheets at:
Topic: Sum of Interior Angles Worksheet 1 a pentagon? nine 3. If the polygon equals 1080, then determine the 1620º? interior angles equals 6840s? n eighteen a Octagon? seventeen polygon equals 1980, how
More informationLine. 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 informationStudy Guide and Review
Fill in the blank in each sentence with the vocabulary term that best completes the sentence. 1. A is a flat surface made up of points that extends infinitely in all directions. A plane is a flat surface
More informationPark Forest Math Team. Meet #3. Geometry. Selfstudy Packet
Park Forest Math Team Meet #3 Selfstudy Packet Problem Categories for this Meet: 1. Mystery: Problem solving 2. : ngle measures in plane figures including supplements and complements 3. Number Theory:
More informationGeo  CH6 Practice Test
Geo  H6 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Find the measure of each exterior angle of a regular decagon. a. 45 c. 18 b. 22.5
More informationSu.a Supported: Identify Determine if polygons. polygons with all sides have all sides and. and angles equal angles equal (regular)
MA.912.G.2 Geometry: Standard 2: Polygons  Students identify and describe polygons (triangles, quadrilaterals, pentagons, hexagons, etc.), using terms such as regular, convex, and concave. They find measures
More informationChapter 3. Chapter 3 Opener. Section 3.1. Big Ideas Math Blue WorkedOut Solutions. Try It Yourself (p. 101) So, the value of x is 112.
Chapter 3 Opener Try It Yourself (p. 101) 1. The angles are vertical. x + 8 120 x 112 o, the value of x is 112. 2. The angles are adjacent. ( x ) + 3 + 43 90 x + 46 90 x 44 o, the value of x is 44. 3.
More informationTessellations. A tessellation is created when a shape is repeated over and over again to cover the plane without any overlaps or gaps.
Tessellations Katherine Sheu A tessellation is created when a shape is repeated over and over again to cover the plane without any overlaps or gaps. 1. The picture below can be extended to a tessellation
More informationINDEX. Arc Addition Postulate,
# 3060 right triangle, 441442, 684 A Absolute value, 59 Acute angle, 77, 669 Acute triangle, 178 Addition Property of Equality, 86 Addition Property of Inequality, 258 Adjacent angle, 109, 669 Adjacent
More informationCK12 Geometry: Exploring Solids
CK12 Geometry: Exploring Solids Learning Objectives Identify different types of solids and their parts. Use Euler s formula to solve problems. Draw and identify different views of solids. Draw and identify
More informationCentroid: 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:
More information1.1 Identify Points, Lines, and Planes
1.1 Identify Points, Lines, and Planes Objective: Name and sketch geometric figures. Key Vocabulary Undefined terms  These words do not have formal definitions, but there is agreement aboutwhat they mean.
More informationSum of the interior angles of a nsided Polygon = (n2) 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 nsided Polygon = (n2) 180 What you need to know: How to use the formula
More information22.1 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 informationTessellations and Tile Patterns
Tessellations and Tile Patterns Definitions: Tessellation covering, or tiling, of a plane with a pattern of figures so there are no overlaps or gaps. Monohedral tiling tessellation made up of congruent
More information1. A student followed the given steps below to complete a construction. Which type of construction is best represented by the steps given above?
1. A student followed the given steps below to complete a construction. Step 1: Place the compass on one endpoint of the line segment. Step 2: Extend the compass from the chosen endpoint so that the width
More informationThe Polygon AngleSum Theorems 55 A equiangular polygon
5 What You ll Learn To classify polygons To find the sums of the measures of the interior and exterior angles of polygons... nd Why To find the measure of an angle of a triangle used in packaging, as
More informationGEOMETRY 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.
More informationPerimeter and Area. An artist uses perimeter and area to determine the amount of materials it takes to produce a piece such as this.
UNIT 10 Perimeter and Area An artist uses perimeter and area to determine the amount of materials it takes to produce a piece such as this. 3 UNIT 10 PERIMETER AND AREA You can find geometric shapes in
More informationINFORMATION 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 informationparallel 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 informationRules of angles (7 9)
Rules of angles (7 9) Contents asic rules of angles Angles in parallel lines (7 9) 3 Angles in polygons (year 9) 4 3. The central angle in a regular polygon...................... 4 3. The exterior angle
More informationEXPLORING GEOMETRIC FIGURES Grade 10 6Day Lesson Plan
1 EXPLORING GEOMETRIC FIGURES Grade 10 6Day Lesson Plan Tangrams Geoboards Equation Grapher Green Globs AlphaShapes Protractor Compass Created by Sandra Metzler 2 OVERALL OBJECTIVES 1 Students will increase
More informationExploring Geometric Figures Using Cabri Geometry II
Exploring Geometric Figures Using Cabri Geometry II Regular Polygons Developed by: Charles Bannister. Chambly County High School Linda Carre.. Chambly County High School Manon Charlebois Vaudreuil Catholic
More informationGeometry Chapter 1. 1.1 Point (pt) 1.1 Coplanar (1.1) 1.1 Space (1.1) 1.2 Line Segment (seg) 1.2 Measure of a Segment
Geometry Chapter 1 Section Term 1.1 Point (pt) Definition A location. It is drawn as a dot, and named with a capital letter. It has no shape or size. undefined term 1.1 Line A line is made up of points
More informationTopics Covered on Geometry Placement Exam
Topics Covered on Geometry Placement Exam  Use segments and congruence  Use midpoint and distance formulas  Measure and classify angles  Describe angle pair relationships  Use parallel lines and transversals
More informationIntermediate 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 informationChapter 1 Basics of Geometry Geometry. For questions 15, draw and label an image to fit the descriptions.
Chapter 1 Basics of Geometry Geometry Name For questions 15, draw and label an image to fit the descriptions. 1. intersecting and Plane P containing but not. 2. Three collinear points A, B, and C such
More informationPROPERTIES 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 information3 rd Six Weeks
Geometry 3 rd Six Weeks 014015 MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY Nov 9 10 11 1 13 61 Angle Measures in Polygons Class: Wksht #1 6 Properties of Parallelograms Class: Wksht # 63 Proving Parallelograms
More informationGeometry 81 Angles of Polygons
. Sum of Measures of Interior ngles Geometry 81 ngles of Polygons 1. Interior angles  The sum of the measures of the angles of each polygon can be found by adding the measures of the angles of a triangle.
More informationLesson 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 informationMath 6: Unit 7: Geometry Notes 2Dimensional 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 informationStudent Name: Teacher: Date: District: MiamiDade County Public Schools. Assessment: 9_12 Mathematics Geometry Exam 1
Student Name: Teacher: Date: District: MiamiDade County Public Schools Assessment: 9_12 Mathematics Geometry Exam 1 Description: GEO Topic 1 Test: Tools of Geometry Form: 201 1. A student followed the
More informationActivities Grades 3 5 ROTATING STRING SHAPES. Make multisided shapes with string. [45 minutes]
Activities Grades 3 5 www.exploratorium.edu/geometryplayground/activities ROTATING STRING SHAPES Make multisided shapes with string. [45 minutes] Materials: String, about 2.5 meters (8 feet) long, tied
More informationLEVEL 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 informationPERIMETER AND AREA. In this unit, we will develop and apply the formulas for the perimeter and area of various twodimensional figures.
PERIMETER AND AREA In this unit, we will develop and apply the formulas for the perimeter and area of various twodimensional figures. Perimeter Perimeter The perimeter of a polygon, denoted by P, is the
More informationGeometry Progress Ladder
Geometry Progress Ladder Maths Makes Sense Foundation Endofyear objectives page 2 Maths Makes Sense 1 2 Endofblock objectives page 3 Maths Makes Sense 3 4 Endofblock objectives page 4 Maths Makes
More informationBASIC GEOMETRY GLOSSARY
BASIC GEOMETRY GLOSSARY Acute angle An angle that measures between 0 and 90. Examples: Acute triangle A triangle in which each angle is an acute angle. Adjacent angles Two angles next to each other that
More informationShape Dictionary YR to Y6
Shape Dictionary YR to Y6 Guidance Notes The terms in this dictionary are taken from the booklet Mathematical Vocabulary produced by the National Numeracy Strategy. Children need to understand and use
More informationLESSON 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 informationMensuration Introduction
Mensuration Introduction Mensuration is the process of measuring and calculating with measurements. Mensuration deals with the determination of length, area, or volume Measurement Types The basic measurement
More informationChapter 3.1 Angles. Geometry. Objectives: Define what an angle is. Define the parts of an angle.
Chapter 3.1 Angles Define what an angle is. Define the parts of an angle. Recall our definition for a ray. A ray is a line segment with a definite starting point and extends into infinity in only one direction.
More informationA segment, ray, line, or plane that is perpendicular to a segment at its midpoint is called a perpendicular bisector. Perpendicular Bisector Theorem
Perpendicular Bisector Theorem A segment, ray, line, or plane that is perpendicular to a segment at its midpoint is called a perpendicular bisector. Converse of the Perpendicular Bisector Theorem If a
More information2. 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 informationGeometry: 11 Day 1 Points, Lines and Planes
Geometry: 11 Day 1 Points, Lines and Planes What are the Undefined Terms? The Undefined Terms are: What is a Point? How is a point named? Example: What is a Line? A line is named two ways. What are the
More informationA geometric construction is a drawing of geometric shapes using a compass and a straightedge.
Geometric Construction Notes A geometric construction is a drawing of geometric shapes using a compass and a straightedge. When performing a geometric construction, only a compass (with a pencil) and a
More informationUpper 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 informationGeometry of Minerals
Geometry of Minerals Objectives Students will connect geometry and science Students will study 2 and 3 dimensional shapes Students will recognize numerical relationships and write algebraic expressions
More informationGeometry Honors: Extending 2 Dimensions into 3 Dimensions. Unit Overview. Student Focus. Semester 2, Unit 5: Activity 30. Resources: Online Resources:
Geometry Honors: Extending 2 Dimensions into 3 Dimensions Semester 2, Unit 5: Activity 30 Resources: SpringBoard Geometry Online Resources: Geometry Springboard Text Unit Overview In this unit students
More informationGeometry  Chapter 2 Review
Name: Class: Date: Geometry  Chapter 2 Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Determine if the conjecture is valid by the Law of Syllogism.
More informationAngles 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