Lesson 7.1. Angles of Polygons

Size: px
Start display at page:

Download "Lesson 7.1. Angles of Polygons"

Transcription

1 Lesson 7.1 Angles of Polygons

2 Essential Question: How can I find the sum of the measures of the interior angles of a polygon?

3 Polygon A plane figure made of three or more segments (sides). Each side intersects exactly two other sides at their endpoints. Polygons are named by vertices in consecutive order, going CW or CCW.

4 Diagonals in a Polygon A segment that joins two non-consecutive vertices. The diagonals from one vertex divide a polygon into triangles.

5 Interior Angle Sum of a Triangle m 1 = m m 2 = m m 4 m 1 + m 5 m 2 + m 3 =

6 Polygon Interior Angle Sums Polygon Sides Triangles formed by Diagonals Sum of Interior Angles Triangle

7 Interiore Angle Sum in a Quadrilateral s 360 m 1 + m 2 + m 3 = m 4 + m 5 + m 6 = 180 m 1 + m 4 + m 2 + m 5 + m 3 + m 6 = 360

8 Polygon Interor Angle Sums Polygon Sides Triangles formed by Diagonals Sum of Interior Angles Triangle Quadrilateral

9 Interior Angle Sum in a Pentagon From this vertex, how many diagonals are there? 2

10 Angle Sum in a Pentagon How many triangles are there? 3 And what is the sum of the angles of each triangle?

11 Angle Sum in a Pentagon 3 s So what is the sum of the interior angles of a pentagon? = 540

12 Polygon Interior Angle Sums Polygon Sides Triangles formed by Diagonals Sum of Interior Angles Triangle Quadrilateral Pentagon

13 Interior Angle Sum in a Hexagon How many diagonals from this vertex? 3 How many triangles are formed? 4 The sum of the angles is? = s 720

14 Polygon Interior Angle Sums Polygon Sides Triangles formed by Diagonals Sum of Interior Angles Triangle Quadrilateral Pentagon Hexagon

15

16 Polygon Interior Angle Sums Polygon Sides Triangles formed by Diagonals Sum of Interior Angles Triangle Quadrilateral Pentagon Hexagon Octagon

17 What s the pattern? A polygon with n sides can be divided into how many triangles? n 2 The sum of the angles then is? 180(n 2)

18 Polygon Interior Angle Sums Polygon Sides Triangles formed by Diagonals Sum of Interior Angles Triangle Quadrilateral Pentagon Hexagon Octagon n-gon n n 2 180(n 2)

19 Theorem 7.1 Polygon Interior Angles Theorem The sum of the interior angles of a convex n- gon is: 180 ( n 2) memorize this!

20 Example 1: Find the sum of the interior angles of a polygon with 14 sides. 180(14 2) = 180(12) = 2160

21 Example 2: The sum of the interior angles of a polygon is How many sides does the polygon have? (n 2) = n 360 = n = 3060 n = 17

22 Example 3: The sum of the interior angles of a polygon is How many sides does the polygon have? (n 2) = n 360 = n = 1980 n = 11

23 Example 4: The sum of the interior angles of a polygon is How many sides does the polygon have? This is not a polygon. 180(n 2) = n 360 = n = 1740 n = Why must this be a whole number?

24 7.1 Corollary to the Polygon Interior Angles Theorem The sum of the interior angles of a quadrilateral is = 360

25 Example 5: Solve for x. x 55 x x + x = 360 2x = 360 2x = 250 x = 125

26 Your Turn Find the value of x in the diagram. x = 360 x = 360 x = 72

27 Regular Polygons

28 Regular Polygon All sides congruent All angles congruent The Sum of the interior angles is 180 (n 2) Since the angles are congruent, the measure of each interior angle in a regular polygon is E I = 180 (n 2) n

29 Example 6: Find the measure of each angle of a regular pentagon (5 2) 180(3)

30 Example 7: Each angle of a regular polygon measures 160. How many sides does the polygon have? 180( n 2) 160 n 180n n 20n 360 n 18

31 Example 8: A home plate for a baseball field is shown. a. Is the polygon regular? Explain your reasoning. The polygon is not equilateral or equiangular. So, the polygon is not regular.

32 Example 8: b. Find the measures of C and E. 180 (n 2) = 180 (5 2) = 540 x + x = 540 2x = 540 2x = 270 x = 135 Therefore, C= 135 and E= 135

33 The Sum of the Exterior Angles This always means using one exterior angle at each vertex. But not this one. This angle or this angle.

34 The Sum of the Exterior Angles Extend only ONE side at each vertex. Exterior Angle Exterior Angle Exterior Angle

35 Theorem 7.2 Polygon Exterior Angles Theorem The sum of the exterior angles of any polygon, one angle at each vertex, is 360. S E = 360 m 1 + m m n = 360

36 Example 9: Find the value of x in the diagram. x + 2x = 360 3x = 360 3x = 204 x = 68

37 Corollary The measure of an exterior angle of a regular polygon with n sides is E = 360 E n

38 Example 10: Find the measure of an exterior angle of a regular 40-gon. Solution: 360/40 = 9

39 Example 15: The trampoline shown is shaped like a regular dodecagon. a. Find the measure of each interior angle. 180 ( n 2) n 180(12 2) = 12 = 180(10) 12 = 1800 =

40 Example 15: The trampoline shown is shaped like a regular dodecagon. b. Find the measure of each exterior angle = 30

41 Summary The sum of the interior angles of an n-gon is 180(n 2). The sum of the exterior angles of any polygon is 360. The measure of an interior angle of a regular polygon is 180(n 2) n The measure of an exterior angle of a regular polygon is 360 n..

1/25 Warm Up Find the value of the indicated measure

1/25 Warm Up Find the value of the indicated measure 1/25 Warm Up Find the value of the indicated measure. 1. 2. 3. 4. Lesson 7.1(2 Days) Angles of Polygons Essential Question: What is the sum of the measures of the interior angles of a polygon? What you

More information

6-1 Properties and Attributes of Polygons

6-1 Properties and Attributes of Polygons 6-1 Properties and Attributes of Polygons Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up 1. A? is a three-sided polygon. triangle 2. A? is a four-sided polygon. quadrilateral Evaluate each expression

More information

Objectives. 6-1 Properties and Attributes of Polygons

Objectives. 6-1 Properties and Attributes of Polygons Objectives Classify polygons based on their sides and angles. Find and use the measures of interior and exterior angles of polygons. side of a polygon vertex of a polygon diagonal regular polygon concave

More information

Angles of Polygons. Essential Question What is the sum of the measures of the interior angles of a polygon?

Angles of Polygons. Essential Question What is the sum of the measures of the interior angles of a polygon? 7.1 Angles of Polygons Essential Question What is the sum of the measures of the interior angles of a polygon? The Sum of the Angle Measures of a Polygon Work with a partner. Use dynamic geometry software.

More information

Warm-Up Exercises. 1. If the measures of two angles of a triangle are 19º and 80º, find the measure of the third angle. ANSWER 81º

Warm-Up Exercises. 1. If the measures of two angles of a triangle are 19º and 80º, find the measure of the third angle. ANSWER 81º Warm-Up Exercises 1. If the measures of two angles of a triangle are 19º and 80º, find the measure of the third angle. 81º 2. Solve (x 2)180 = 1980. 13 Warm-Up Exercises 3. Find the value of x. 126 EXAMPLE

More information

Geometry Ch 7 Quadrilaterals January 06, 2016

Geometry Ch 7 Quadrilaterals January 06, 2016 Theorem 17: Equal corresponding angles mean that lines are parallel. Corollary 1: Equal alternate interior angles mean that lines are parallel. Corollary 2: Supplementary interior angles on the same side

More information

Polygons are named by the number of sides they have:

Polygons are named by the number of sides they have: Unit 5 Lesson 1 Polygons and Angle Measures I. What is a polygon? (Page 322) A polygon is a figure that meets the following conditions: It is formed by or more segments called, such that no two sides with

More information

Warm-Up Exercises. 1. Draw an acute angle and shade the interior. ANSWER. 2. Find the measure of the supplement of a 130º angle.

Warm-Up Exercises. 1. Draw an acute angle and shade the interior. ANSWER. 2. Find the measure of the supplement of a 130º angle. Warm-Up Exercises 1. Draw an acute angle and shade the interior. ANSWER 2. Find the measure of the supplement of a 130º angle. ANSWER 50 3. Find the measure of the complement of an 86 angle. ANSWER 4 1.6

More information

Review Interior Angle Sum New: Exterior Angle Sum

Review Interior Angle Sum New: Exterior Angle Sum Review Interior Angle Sum New: Exterior Angle Sum QUIZ: Prove that the diagonal connecting the vertex angles of a kite cut the kite into two congruent triangles. 1 Interior Angle Sum Formula: Some Problems

More information

Geometry Unit 6 Properties of Quadrilaterals Classifying Polygons Review

Geometry Unit 6 Properties of Quadrilaterals Classifying Polygons Review Geometry Unit 6 Properties of Quadrilaterals Classifying Polygons Review Polygon a closed plane figure with at least 3 sides that are segments -the sides do not intersect except at the vertices N-gon -

More information

Geometry/Trigonometry Unit 5: Polygon Notes Period:

Geometry/Trigonometry Unit 5: Polygon Notes Period: Geometry/Trigonometry Unit 5: Polygon Notes Name: Date: Period: # (1) Page 270 271 #8 14 Even, #15 20, #27-32 (2) Page 276 1 10, #11 25 Odd (3) Page 276 277 #12 30 Even (4) Page 283 #1-14 All (5) Page

More information

Polygon. Note: Each segment is called a side. Each endpoint is called a vertex.

Polygon. Note: Each segment is called a side. Each endpoint is called a vertex. Polygons Polygon A closed plane figure formed by 3 or more segments. Each segment intersects exactly 2 other segments at their endpoints. No 2 segments with a common endpoint are collinear. Note: Each

More information

U4 Polygon Notes January 11, 2017 Unit 4: Polygons

U4 Polygon Notes January 11, 2017 Unit 4: Polygons Unit 4: Polygons 180 Complimentary Opposite exterior Practice Makes Perfect! Example: Example: Practice Makes Perfect! Def: Midsegment of a triangle - a segment that connects the midpoints of two sides

More information

Cambridge Essentials Mathematics Core 9 GM1.1 Answers. 1 a

Cambridge Essentials Mathematics Core 9 GM1.1 Answers. 1 a GM1.1 Answers 1 a b 2 Shape Name Regular Irregular Convex Concave A Decagon B Octagon C Pentagon D Quadrilateral E Heptagon F Hexagon G Quadrilateral H Triangle I Triangle J Hexagon Original Material Cambridge

More information

Polygon Angle-Sum Theorem:

Polygon Angle-Sum Theorem: Name Must pass Mastery Check by: [PACKET 5.1: POLYGON -SUM THEOREM] 1 Write your questions here! We all know that the sum of the angles of a triangle equal 180. What about a quadrilateral? A pentagon?

More information

Angles of Polygons. b. Draw other polygons and find the sums of the measures of their interior angles. Record your results in the table below.

Angles of Polygons. b. Draw other polygons and find the sums of the measures of their interior angles. Record your results in the table below. 7.1 TEXS ESSENTIL KNOWLEGE N SKILLS G.5. ngles of Polygons Essential Question What is the sum of the measures of the interior angles of a polygon? of the exterior angles of a polygon? Interior ngle Measures

More information

Geometry Reasons for Proofs Chapter 1

Geometry Reasons for Proofs Chapter 1 Geometry Reasons for Proofs Chapter 1 Lesson 1.1 Defined Terms: Undefined Terms: Point: Line: Plane: Space: Postulate 1: Postulate : terms that are explained using undefined and/or other defined terms

More information

A closed plane figure with at least 3 sides The sides intersect only at their endpoints. Polygon ABCDEF

A closed plane figure with at least 3 sides The sides intersect only at their endpoints. Polygon ABCDEF A closed plane figure with at least 3 sides The sides intersect only at their endpoints B C A D F E Polygon ABCDEF The diagonals of a polygon are the segments that connects one vertex of a polygon to another

More information

heptagon; not regular; hexagon; not regular; quadrilateral; convex concave regular; convex

heptagon; not regular; hexagon; not regular; quadrilateral; convex concave regular; convex 10 1 Naming Polygons A polygon is a plane figure formed by a finite number of segments. In a convex polygon, all of the diagonals lie in the interior. A regular polygon is a convex polygon that is both

More information

PLC Papers Created For:

PLC Papers Created For: PLC Papers Created For: Year 10 Topic Practice Papers: Polygons Polygons 1 Grade 4 Look at the shapes below A B C Shape A, B and C are polygons Write down the mathematical name for each of the polygons

More information

2.4 Angle Properties in Polygons.notebook. October 27, 2013 ENTRANCE SLIP

2.4 Angle Properties in Polygons.notebook. October 27, 2013 ENTRANCE SLIP ENTRANCE SLIP If you are given one interior angle and one exterior angle of a triangle, can you always determine the other interior angles of the triangle? Explain, using diagrams. 1 2.4 Angle Properties

More information

Polygons. L E S S O N 1.4

Polygons.  L E S S O N 1.4 Page 1 of 5 L E S S O N 1.4 Polygons A polygon is a closed figure in a plane, formed by connecting line segments endpoint to endpoint with each segment intersecting exactly two others. Each line segment

More information

Unit 10 Study Guide: Plane Figures

Unit 10 Study Guide: Plane Figures Unit 10 Study Guide: Plane Figures *Be sure to watch all videos within each lesson* You can find geometric shapes in art. Whether determining the amount of leading or the amount of glass needed for a piece

More information

Lesson Plan #39. 2) Students will be able to find the sum of the measures of the exterior angles of a triangle.

Lesson Plan #39. 2) Students will be able to find the sum of the measures of the exterior angles of a triangle. Lesson Plan #39 Class: Geometry Date: Tuesday December 11 th, 2018 Topic: Sum of the measures of the interior angles of a polygon Objectives: Aim: What is the sum of the measures of the interior angles

More information

Angle Unit Definition Packet

Angle Unit Definition Packet ngle Unit Definition Packet Name lock Date Term Definition Notes Sketch djacent ngles Two angles with a coon, a coon you normay name and, and no coon interior points. 3 4 3 and 4 Vertical ngles Two angles

More information

Angles in a polygon Lecture 419

Angles in a polygon Lecture 419 Angles in a polygon Lecture 419 Formula For an n-sided polygon, the number of degrees for the sum of the internal angles is 180(n-2)º. For n=3 (triangle), it's 180. For n=4 (quadrilateral), it's 360. And

More information

Any questions about the material so far? About the exercises?

Any questions about the material so far? About the exercises? Any questions about the material so far? About the exercises? Here is a question for you. In the diagram on the board, DE is parallel to AC, DB = 4, AB = 9 and BE = 8. What is the length EC? Polygons Definitions:

More information

8 Quadrilaterals. Before

8 Quadrilaterals. Before 8 Quadrilaterals 8. Find Angle Measures in Polygons 8. Use Properties of Parallelograms 8.3 Show that a Quadrilateral is a Parallelogram 8.4 Properties of Rhombuses, Rectangles, and Squares 8.5 Use Properties

More information

Math Polygons

Math Polygons Math 310 9.2 Polygons Curve & Connected Idea The idea of a curve is something you could draw on paper without lifting your pencil. The idea of connected is that a set can t be split into two disjoint sets.

More information

Chapter 1-2 Points, Lines, and Planes

Chapter 1-2 Points, Lines, and Planes Chapter 1-2 Points, Lines, and Planes Undefined Terms: A point has no size but is often represented by a dot and usually named by a capital letter.. A A line extends in two directions without ending. Lines

More information

7.1 Start Thinking. 7.1 Warm Up. 7.1 Cumulative Review Warm Up

7.1 Start Thinking. 7.1 Warm Up. 7.1 Cumulative Review Warm Up 7.1 Start Thinking The polygon in the diagram has been formed by adjoining triangles. Use your knowledge of the sum of the measures of the interior angles of a triangle to determine the sum of the measures

More information

Geometry Review for Test 3 January 13, 2016

Geometry Review for Test 3 January 13, 2016 Homework #7 Due Thursday, 14 January Ch 7 Review, pp. 292 295 #1 53 Test #3 Thurs, 14 Jan Emphasis on Ch 7 except Midsegment Theorem, plus review Betweenness of Rays Theorem Whole is Greater than Part

More information

Geometry Chapter 8 Test Review

Geometry Chapter 8 Test Review Geometry Chapter 8 Test Review Short Answer 1. Find the sum of the measures of the interior angles of the indicated convex polygon. Decagon 2. Find the sum of the measures of the interior angles of the

More information

Explore 2 Exploring Interior Angles in Polygons

Explore 2 Exploring Interior Angles in Polygons Explore 2 Exploring Interior Angles in Polygons To determine the sum of the interior angles for any polygon, you can use what you know about the Triangle Sum Theorem by considering how many triangles there

More information

Angle Unit Definitions

Angle Unit Definitions ngle Unit Definitions Name lock Date Term Definition Notes Sketch D djacent ngles Two coplanar angles with a coon side, a coon vertex, and no coon interior points. Must be named with 3 letters OR numbers

More information

Convex polygon - a polygon such that no line containing a side of the polygon will contain a point in the interior of the polygon.

Convex polygon - a polygon such that no line containing a side of the polygon will contain a point in the interior of the polygon. Chapter 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

1.6 Classifying Polygons

1.6 Classifying Polygons www.ck12.org Chapter 1. Basics of Geometry 1.6 Classifying Polygons Learning Objectives Define triangle and polygon. Classify triangles by their sides and angles. Understand the difference between convex

More information

6 Polygons and. Quadrilaterals CHAPTER. Chapter Outline.

6 Polygons and. Quadrilaterals CHAPTER. Chapter Outline. www.ck12.org CHAPTER 6 Polygons and Quadrilaterals Chapter Outline 6.1 ANGLES IN POLYGONS 6.2 PROPERTIES OF PARALLELOGRAMS 6.3 PROVING QUADRILATERALS ARE PARALLELOGRAMS 6.4 RECTANGLES, RHOMBUSES AND SQUARES

More information

Special Lines and Constructions of Regular Polygons

Special Lines and Constructions of Regular Polygons Special Lines and Constructions of Regular Polygons A regular polygon with a center A is made up of congruent isosceles triangles with a principal angle A. The red line in the regular pentagon below is

More information

First we need a more precise, rigorous definition:

First we need a more precise, rigorous definition: Lesson 21 Lesson 20, page 1 of 8 Glencoe Geometry Chapter 10.1 Polygons & Area We have been working with special types of polygons throughout the year. Rectangles, Squares, Trapezoids, and, yes, Triangles

More information

MPM1D Page 1 of 6. length, width, thickness, area, volume, flatness, infinite extent, contains infinite number of points. A part of a with endpoints.

MPM1D Page 1 of 6. length, width, thickness, area, volume, flatness, infinite extent, contains infinite number of points. A part of a with endpoints. MPM1D Page 1 of 6 Unit 5 Lesson 1 (Review) Date: Review of Polygons Activity 1: Watch: http://www.mathsisfun.com/geometry/dimensions.html OBJECT Point # of DIMENSIONS CHARACTERISTICS location, length,

More information

Term Definition Figure

Term Definition Figure Notes LT 1.1 - Distinguish and apply basic terms of geometry (coplanar, collinear, bisectors, congruency, parallel, perpendicular, etc.) Term Definition Figure collinear on the same line (note: you do

More information

Click the mouse button or press the Space Bar to display the answers.

Click the mouse button or press the Space Bar to display the answers. Click the mouse button or press the Space Bar to display the answers. 9-4 Objectives You will learn to: Identify regular tessellations. Vocabulary Tessellation Regular Tessellation Uniform Semi-Regular

More information

Unit 2: Triangles and Quadrilaterals Lesson 2.1 Apply Triangle Sum Properties Lesson 4.1 from textbook

Unit 2: Triangles and Quadrilaterals Lesson 2.1 Apply Triangle Sum Properties Lesson 4.1 from textbook Unit 2: Triangles and Quadrilaterals Lesson 2.1 pply Triangle Sum Properties Lesson 4.1 from textbook Objectives Classify angles by their sides as equilateral, isosceles, or scalene. Classify triangles

More information

Lesson Polygons

Lesson Polygons Lesson 4.1 - Polygons Obj.: classify polygons by their sides. classify quadrilaterals by their attributes. find the sum of the angle measures in a polygon. Decagon - A polygon with ten sides. Dodecagon

More information

Chapter 3 Final Review

Chapter 3 Final Review Class: Date: Chapter 3 Final Review Multiple Choice Identify the choice that best completes the statement or answers the question. Find the sum of the interior angle measures of the polygon. 1. a. 360

More information

MAT104: Fundamentals of Mathematics II Introductory Geometry Terminology Summary. Section 11-1: Basic Notions

MAT104: Fundamentals of Mathematics II Introductory Geometry Terminology Summary. Section 11-1: Basic Notions MAT104: Fundamentals of Mathematics II Introductory Geometry Terminology Summary Section 11-1: Basic Notions Undefined Terms: Point; Line; Plane Collinear Points: points that lie on the same line Between[-ness]:

More information

Polygons and Convexity

Polygons and Convexity Geometry Week 4 Sec 2.5 to ch. 2 test Polygons and Convexity section 2.5 convex set has the property that any two of its points determine a segment contained in the set concave set a set that is not convex

More information

Chapter Review. In the figure shown, m n and r is a transversal. If m 4 = 112, find the measure of each angle. Explain your reasoning.

Chapter Review. In the figure shown, m n and r is a transversal. If m 4 = 112, find the measure of each angle. Explain your reasoning. In the figure shown, m n and r is a transversal. If m 4 = 112, find the measure of each angle. Explain your reasoning. 1. 6 Since 4 and 6 are alternate interior angles, they are congruent. So, m 6 = 112.

More information

6.7 Regular Polygons

6.7 Regular Polygons 6.7 Regular Polygons Dec 13 3:08 PM 1 Recall, what is a polygon? A union of segments in the same plane such that each segment intersects two others, one at each of its endpoints Dec 13 3:13 PM 2 Define

More information

Lines Plane A flat surface that has no thickness and extends forever.

Lines Plane A flat surface that has no thickness and extends forever. Lines Plane A flat surface that has no thickness and extends forever. Point an exact location Line a straight path that has no thickness and extends forever in opposite directions Ray Part of a line that

More information

14. How many sides does a regular polygon have, if the measure of an interior angle is 60?

14. How many sides does a regular polygon have, if the measure of an interior angle is 60? State whether the figure is a polygon; if it is a polygon, state whether the polygon is convex or concave. HINT: No curves, no gaps, and no overlaps! 1. 2. 3. 4. Find the indicated measures of the polygon.

More information

8.1 Find Angle Measures in Polygons

8.1 Find Angle Measures in Polygons VOCABULARY 8.1 Find Angle Measures in Polygons DIAGONAL Review: EQUILATERAL EQUIANGULAR REGULAR CLASSIFYING POLYGONS Polygon Interior Angle Theorem: The sum of the measures of the interior angles of a

More information

6.1: Date: Geometry. Polygon Number of Triangles Sum of Interior Angles

6.1: Date: Geometry. Polygon Number of Triangles Sum of Interior Angles 6.1: Date: Geometry Polygon Number of Triangles Sum of Interior Angles Triangle: # of sides: # of triangles: Quadrilateral: # of sides: # of triangles: Pentagon: # of sides: # of triangles: Hexagon: #

More information

1. Revision Description Reflect and Review Teasers Answers Recall of basics of triangles, polygons etc. Review Following are few examples of polygons:

1. Revision Description Reflect and Review Teasers Answers Recall of basics of triangles, polygons etc. Review Following are few examples of polygons: 1. Revision Recall of basics of triangles, polygons etc. The minimum number of line segments required to form a polygon is 3. 1) Name the polygon formed with 4 line segments of equal length. 1) Square

More information

Geometry. Kites Families of Quadrilaterals Coordinate Proofs Proofs. Click on a topic to

Geometry. Kites Families of Quadrilaterals Coordinate Proofs Proofs. Click on a topic to Geometry Angles of Polygons Properties of Parallelograms Proving Quadrilaterals are Parallelograms Constructing Parallelograms Rhombi, Rectangles and Squares Kites Families of Quadrilaterals Coordinate

More information

ame Date Class Practice A 11. What is another name for a regular quadrilateral with four right angles?

ame Date Class Practice A 11. What is another name for a regular quadrilateral with four right angles? ame Date Class Practice A Polygons Name each polygon. 1. 2. 3. 4. 5. 6. Tell whether each polygon appears to be regular or not regular. 7. 8. 9. 10. What is another name for a regular triangle? 11. What

More information

Chapter 10 Polygons and Area

Chapter 10 Polygons and Area Geometry Concepts Chapter 10 Polygons and Area Name polygons according to sides and angles Find measures of interior angles Find measures of exterior angles Estimate and find areas of polygons Estimate

More information

Circles and Polygons Long-Term Memory Review Review 1 (Note: Figures are not drawn to scale.)

Circles and Polygons Long-Term Memory Review Review 1 (Note: Figures are not drawn to scale.) Review 1 (Note: Figures are not drawn to scale.) 1. Fill in the lank: In circle below, the angle shown is a/an angle. 2. The measure of a central angle and the measure of the arc that it intersects are

More information

Postulates, Theorems, and Corollaries. Chapter 1

Postulates, Theorems, and Corollaries. Chapter 1 Chapter 1 Post. 1-1-1 Through any two points there is exactly one line. Post. 1-1-2 Through any three noncollinear points there is exactly one plane containing them. Post. 1-1-3 If two points lie in a

More information

Ch. 7 Test. 1. Find the sum of the measures of the interior angles of the given figure.

Ch. 7 Test. 1. Find the sum of the measures of the interior angles of the given figure. h. 7 Test 1. Find the sum of the measures of the interior angles of the given figure. a. 900 c. 70 b. 10 d. 1080. The sum of the measures of the interior angles of a polygon is 10. lassify the polygon

More information

If lines m and n are parallel, we write. Transversal: A line that INTERSECTS two or more lines at 2

If lines m and n are parallel, we write. Transversal: A line that INTERSECTS two or more lines at 2 Unit 4 Lesson 1: Parallel Lines and Transversals Name: COMPLEMENTARY are angles to add up to 90 SUPPLEMENTARY are angles to add up to 180 These angles are also known as a LINEAR PAIR because they form

More information

Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 1 AND

Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 1 AND Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 1 AND Chapter 9 Geometry Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 2 WHAT YOU WILL LEARN Points, lines, planes, and

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

Unit 6 Polygons and Quadrilaterals

Unit 6 Polygons and Quadrilaterals 6.1 What is a Polygon? A closed plane figure formed by segments that intersect only at their endpoints Regular Polygon- a polygon that is both equiangular and equilateral Unit 6 Polygons and Quadrilaterals

More information

Answer Key. 1.1 Basic Geometric Definitions. Chapter 1 Basics of Geometry. CK-12 Geometry Concepts 1

Answer Key. 1.1 Basic Geometric Definitions. Chapter 1 Basics of Geometry. CK-12 Geometry Concepts 1 1.1 Basic Geometric Definitions 1. WX, XW, WY, YW, XY, YX and line m. 2. Plane V, Plane RST, Plane RTS, Plane STR, Plane SRT, Plane TSR, and Plane TRS. 3. 4. A Circle 5. PQ intersects RS at point Q 6.

More information

Points, lines, angles

Points, lines, angles Points, lines, angles Point Line Line segment Parallel Lines Perpendicular lines Vertex Angle Full Turn An exact location. A point does not have any parts. A straight length that extends infinitely in

More information

Unit 3: Triangles and Polygons

Unit 3: Triangles and Polygons Unit 3: Triangles and Polygons Background for Standard G.CO.9: Prove theorems about triangles. Objective: By the end of class, I should Example 1: Trapezoid on the coordinate plane below has the following

More information

Unit 3 Geometry. Chapter 7 Geometric Relationships Chapter 8 Measurement Relationships Chapter 9 Optimizing Measurements MPM1D

Unit 3 Geometry. Chapter 7 Geometric Relationships Chapter 8 Measurement Relationships Chapter 9 Optimizing Measurements MPM1D Unit 3 Geometry Chapter 7 Geometric Relationships Chapter 8 Measurement Relationships Chapter 9 Optimizing Measurements MPM1D Chapter 7 Outline Section Subject Homework Notes Lesson and Homework Complete

More information

GEOMETRY is the study of points in space

GEOMETRY is the study of points in space CHAPTER 5 Logic and Geometry SECTION 5-1 Elements of Geometry GEOMETRY is the study of points in space POINT indicates a specific location and is represented by a dot and a letter R S T LINE is a set of

More information

Geometry Basics of Geometry Precise Definitions Unit CO.1 OBJECTIVE #: G.CO.1

Geometry Basics of Geometry Precise Definitions Unit CO.1 OBJECTIVE #: G.CO.1 OBJECTIVE #: G.CO.1 OBJECTIVE Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance

More information

Tessellations: Wallpapers, Escher & Soccer Balls. Robert Campbell

Tessellations: Wallpapers, Escher & Soccer Balls. Robert Campbell Tessellations: Wallpapers, Escher & Soccer Balls Robert Campbell Tessellation Examples What Is What is a Tessellation? A Tessellation (or tiling) is a pattern made by copies of one or

More information

Polygons. Discuss with a partner what a POLYGON is. Write down the key qualities a POLYGON has. Share with the class what a polygon is?

Polygons. Discuss with a partner what a POLYGON is. Write down the key qualities a POLYGON has. Share with the class what a polygon is? Polygons Use a ruler to draw 3 different POLYGONS Discuss with a partner what a POLYGON is Write down the key qualities a POLYGON has Share with the class what a polygon is? *Can you find the area of each

More information

Lesson 4.3 Ways of Proving that Quadrilaterals are Parallelograms

Lesson 4.3 Ways of Proving that Quadrilaterals are Parallelograms Lesson 4.3 Ways of Proving that Quadrilaterals are Parallelograms Getting Ready: How will you know whether or not a figure is a parallelogram? By definition, a quadrilateral is a parallelogram if it has

More information

Grade 8 Math WORKBOOK UNIT 1 : POLYGONS. Are these polygons? Justify your answer by explaining WHY or WHY NOT???

Grade 8 Math WORKBOOK UNIT 1 : POLYGONS. Are these polygons? Justify your answer by explaining WHY or WHY NOT??? Grade 8 Math WORKBOOK UNIT 1 : 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

More information

Maintaining Mathematical Proficiency

Maintaining Mathematical Proficiency Name ate hapter 7 Maintaining Mathematical Proficiency Solve the equation by interpreting the expression in parentheses as a single quantity. 1. 5( 10 x) = 100 2. 6( x + 8) 12 = 48 3. ( x) ( x) 32 + 42

More information

Section 9.1. Points, Lines, Planes, and Angles. Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Section 9.1. Points, Lines, Planes, and Angles. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 9.1 Points, Lines, Planes, and Angles What You Will Learn Points Lines Planes Angles 9.1-2 Basic Terms A point, line, and plane are three basic terms in geometry that are NOT given a formal definition,

More information

Examples: Identify the following as equilateral, equiangular or regular. Using Variables: S = 180(n 2)

Examples: Identify the following as equilateral, equiangular or regular. Using Variables: S = 180(n 2) Ch. 6 Notes 6.1: Polygon Angle-Sum Theorems Examples: Identify the following as equilateral, equiangular or regular. 1) 2) 3) S = 180(n 2) Using Variables: and Examples: Find the sum of the interior angles

More information

Sum of the Interior Angle Measures This coin was the first to show the image of a real woman.

Sum of the Interior Angle Measures This coin was the first to show the image of a real woman. Interior Angles of a Polygon Sum of the Interior Angle Measures of a Polygon.4 Learning Goals Key Term In this lesson, you will: Write the formula for the sum of the measures of the interior angles of

More information

4.1 TRIANGLES AND ANGLES

4.1 TRIANGLES AND ANGLES 4.1 TRIANGLES AND ANGLES polygon- a closed figure in a plane that is made up of segments, called sides, that intersect only at their endpoints, called vertices Can you name these? triangle- a three-sided

More information

STANDARDS OF LEARNING CONTENT REVIEW NOTES HONORS GEOMETRY. 3 rd Nine Weeks,

STANDARDS OF LEARNING CONTENT REVIEW NOTES HONORS GEOMETRY. 3 rd Nine Weeks, STANDARDS OF LEARNING CONTENT REVIEW NOTES HONORS GEOMETRY 3 rd Nine Weeks, 2016-2017 1 OVERVIEW Geometry Content Review Notes are designed by the High School Mathematics Steering Committee as a resource

More information

Polygons. Discuss with a partner what a POLYGON is. Write down the key qualities a POLYGON has. Share with the class what a polygon is?

Polygons. Discuss with a partner what a POLYGON is. Write down the key qualities a POLYGON has. Share with the class what a polygon is? Polygons Use a ruler to draw 3 different POLYGONS Discuss with a partner what a POLYGON is Write down the key qualities a POLYGON has Share with the class what a polygon is? *Can you find the area of each

More information

Geometry. Quadrilaterals. Slide 1 / 189. Slide 2 / 189. Slide 3 / 189. Table of Contents. New Jersey Center for Teaching and Learning

Geometry. Quadrilaterals. Slide 1 / 189. Slide 2 / 189. Slide 3 / 189. Table of Contents. New Jersey Center for Teaching and Learning New Jersey enter for Teaching and Learning Slide 1 / 189 Progressive Mathematics Initiative This material is made freely available at www.njctl.org and is intended for the non-commercial use of students

More information

Chapter 2 QUIZ. Section 2.1 The Parallel Postulate and Special Angles

Chapter 2 QUIZ. Section 2.1 The Parallel Postulate and Special Angles Chapter 2 QUIZ Section 2.1 The Parallel Postulate and Special Angles (1.) How many lines can be drawn through point P that are parallel to line? (2.) Lines and m are cut by transversal t. Which angle corresponds

More information

Geometry Unit 2 Test , 3.8,

Geometry Unit 2 Test , 3.8, Name: Class: Date: ID: A Geometry Unit 2 Test - 3.1-3.5, 3.8, 9.1-9.3 Short Answer - You are allowed to use your notes and calculator. No cell phones.good luck! 1. Line r is parallel to line t. Find m

More information

CK-12 Geometry: Similar Polygons

CK-12 Geometry: Similar Polygons CK-12 Geometry: Similar Polygons Learning Objectives Recognize similar polygons. Identify corresponding angles and sides of similar polygons from a similarity statement. Calculate and apply scale factors.

More information

4-8 Notes. Warm-Up. Discovering the Rule for Finding the Total Degrees in Polygons. Triangles

4-8 Notes. Warm-Up. Discovering the Rule for Finding the Total Degrees in Polygons. Triangles Date: Learning Goals: How do you find the measure of the sum of interior and exterior angles in a polygon? How do you find the measures of the angles in a regular polygon? Warm-Up 1. What is similar about

More information

Angles, Polygons, Circles

Angles, Polygons, Circles Page 1 of 5 Part One Last week we learned about the angle properties of circles and used them to solve a simple puzzle. This week brings a new puzzle that will make us use our algebra a bit more. But first,

More information

You can use theorems about the interior and exterior angles of convex polygons to solve problems.

You can use theorems about the interior and exterior angles of convex polygons to solve problems. 8 Big Idea CATER SUMMARY BI IDEAS Using Angle Relationships in olygons You can use theorems about the interior and exterior angles of convex polygons to solve problems. or Your Notebook olygon Interior

More information

What is a tessellation???? Give an example... Daily Do from last class Homework Answers 10 7 These are similar: What does y =? x =?

What is a tessellation???? Give an example... Daily Do from last class Homework Answers 10 7 These are similar: What does y =? x =? Daily Do from last class Homework Answers 10 7 These are similar: What does y =? x =? 36 74 0 78 0 154 o 44 48 54 o y x 154 o 78 0 12 74 0 9 1. 8 ft 2. 21m 3. 21 ft 4. 30cm 5. 6mm 6. 16 in 7. yes 9 = 7

More information

Math 366 Lecture Notes Section 11.4 Geometry in Three Dimensions

Math 366 Lecture Notes Section 11.4 Geometry in Three Dimensions Math 366 Lecture Notes Section 11.4 Geometry in Three Dimensions Simple Closed Surfaces A simple closed surface has exactly one interior, no holes, and is hollow. A sphere is the set of all points at a

More information

Yimin Math Centre. 6.1 Properties of geometrical figures Recognising plane shapes... 1

Yimin Math Centre. 6.1 Properties of geometrical figures Recognising plane shapes... 1 Yimin Math Centre Student Name: Grade: Date: Score: Table of Contents 6 Year 7 Term 3 Week 6 Homework 1 6.1 Properties of geometrical figures............................ 1 6.1.1 Recognising plane shapes...........................

More information

Secondary Math II Honors. Unit 4 Notes. Polygons. Name: Per:

Secondary Math II Honors. Unit 4 Notes. Polygons. Name: Per: Secondary Math II Honors Unit 4 Notes Polygons Name: Per: Day 1: Interior and Exterior Angles of a Polygon Unit 4 Notes / Secondary 2 Honors Vocabulary: Polygon: Regular Polygon: Example(s): Discover the

More information

9.5 Classifying Polygons

9.5 Classifying Polygons www.ck12.org Chapter 9. Geometric Figures 9.5 Classifying Polygons Introduction The Sculpture Courtesy of Martin Fuchs Marc, Isaac and Isabelle continue to work on their design for the skatepark. Isabelle

More information

Proving Theorems about Lines and Angles

Proving Theorems about Lines and Angles Proving Theorems about Lines and Angles Angle Vocabulary Complementary- two angles whose sum is 90 degrees. Supplementary- two angles whose sum is 180 degrees. Congruent angles- two or more angles with

More information

An angle that has a measure less than a right angle.

An angle that has a measure less than a right angle. Unit 1 Study Strategies: Two-Dimensional Figures Lesson Vocab Word Definition Example Formed by two rays or line segments that have the same 1 Angle endpoint. The shared endpoint is called the vertex.

More information

Unit 4 Quadrilaterals and Polygons (QDP) Target Lesson Plan 3 Weeks

Unit 4 Quadrilaterals and Polygons (QDP) Target Lesson Plan 3 Weeks Unit 4 Quadrilaterals and Polygons (QDP) Target Lesson Plan 3 Weeks 2011-12 M2.3.J Know, prove, and apply basic theorems about s. 2,3 MC,CP I Know, prove, and apply theorems about properties of quadrilaterals

More information

Assumption High School. Bell Work. Academic institution promoting High expectations resulting in Successful students

Assumption High School. Bell Work. Academic institution promoting High expectations resulting in Successful students Bell Work Geometry 2016 2017 Day 36 Topic: Chapter 4 Congruent Figures Chapter 6 Polygons & Quads Chapter 4 Big Ideas Visualization Visualization can help you connect properties of real objects with two-dimensional

More information

Section 4: Introduction to Polygons Part 1

Section 4: Introduction to Polygons Part 1 The following Mathematics Florida Standards will be covered in this section: MAFS.912.G-CO.1.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the

More information

AN INNOVATIVE ANALYSIS TO DEVELOP NEW THEOREMS ON IRREGULAR POLYGON

AN INNOVATIVE ANALYSIS TO DEVELOP NEW THEOREMS ON IRREGULAR POLYGON International Journal of Physics and Mathematical Sciences ISSN: 77-111 (Online) 013 Vol. 3 (1) January-March, pp.73-81/kalaimaran AN INNOVATIVE ANALYSIS TO DEVELOP NEW THEOREMS ON IRREGULAR POLYGON *Kalaimaran

More information