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

Size: px
Start display at page:

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

Transcription

1

2 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?

3 Polygons Definitions: A polygon is a closed plane figure whose sides are line segments. Points where two segments meet are called vertices. The angles formed inside the polygon are called interior angles. A polygon is regular if all its sides and interior angles are congruent. Note: A polygon with three sides is a triangle, with four sides it is called a quadrilateral; with fives sides, it is a pentagon.

4 NUMBER OF SIDES POLYGON 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon 8 Octagon 9 Nonagon 10 Decagon 12 Dodecagon n n-gon

5 Theorem: The sum of the interior angles of a n-gon is Proof: (n - 2)180 Pick a vertex and then draw a line segment to each of the other vertices as shown above forming some triangles. Note that that the first and last triangles formed contain two sides of the polygon but each of the others contain only one side. Thus there are two fewer triangles than there are sides; i.e., if there are n sides, then there are n - 2 triangles formed. Since each triangle has 180 degrees and there are n - 2 of them, the total for the polygon is (n - 2)180.

6 The sum of the interior angles of a quadrilateral is (4-2)180 = 360 degrees. The sum of the interior angles of a pentagon is (5-2)180 = 540 degrees. Etc. Sum of exterior angles of an n-gon = 180n degrees.

7 Quadrilaterals A quadrilateral is any four-sided polygon but certain ones with specific restrictions are most important for us. Definition: A parallelogram is a quadrilateral whose opposite sides are parallel. A B C D A diagonal divides it into two triangles. Are the triangles congruent? Why? It follows now that the opposite sides of a parallelogram are congruent. Likewise, the opposite angles are congruent and the consecutive angles are supplementary. Converses true?

8 Theorem: The diagonals of a parallelogram bisect each other. Proof:? Question: Is the converse true? That is, if the diagonals of a quadrilateral bisect each other, must the quadrilateral be a parallelogram?

9 Definition: A parallelogram with all four sides congruent is called a rhombus. Definition: A parallelogram with all four angles congruent (each is 90 ) is called a. rectangle Definition: A rectangle with all four sides congruent is called a square.

10 Diagonals Parallelogram Rectangle Rhombus Square Bisect each other X X X X Are congruent X X Are perpendicular X X Bisect vertex angles X X Form 2 pairs of congruent triangles X X X X Form 4 congruent triangles X X

11 Areas A square unit is the surface enclosed by a square whose side measures 1 unit (like inches, feet, or some arbitrary scale.) The area of a polygon is the number of square units contained within its boundary. Area of a Rectangle: Pick one of the sides and call it the base and one of the sides perpendicular to it and call it the height. For example, if the base is 5 units and the height is 4 units, then we can fit 5x4 = 20 square units inside; so its area is 20. height = 4 units Area = 20 sq. units base = 5 units

12 Since a rectangle with a base b units long and height h units high contains bh square units, we know that The area A of a rectangle with base b a height h is A = bh Note: We sometimes use the letter A for a vertex and also for the area so make sure of the context. The area of a square with side s is A = s 2. Problem: How many square inches are there in 1 square foot? Problem: What is the area of a square with a perimeter of 36 units?

13 Area of a Parallelogram Definition: In a parallelogram, pick one of the sides and call it a base. The height is a segment from a point on the opposite side and drawn perpendicular to that base. h b Theorem: The area of a parallelogram is the base times the height; i.e., A = bh. Proof? Problem: Find the base of a parallelogram whose area is 27 and the base is three times the height.

14 Area of a Triangle In a triangle, pick one of the sides and call it the base. From the opposite vertex draw a segment perpendicular to the base; we call this the height of the triangle. h h b b Theorem: The area of a triangle is 1/2 the base times the height; A = bh/2 Proof? Problem: Find the area of a triangle whose sides are 3,4 and 5 units.

15 Area of a Trapezoid Definitions. A trapezoid is a quadrilateral with only two sides parallel; the parallel sides are called the bases and the height is a segment from one base drawn perpendicular to the other base. b h b Theorem: The area of a trapezoid is 1/2 the sum of the bases times the height; A = (b + b )h/2. Proof? Problem: What is the height of a trapezoid with bases 13 and 7 and area 40?

16 Exercises 1. What is the sum of the interior angles of an octagon? 2. What is the measure of an interior angle of a regular pentagon. 3. Prove that if the perpendiculars to two sides of a triangle from the midpoint of the third side are congruent, then the triangle is isosceles. 4. Find the area of a rectangle with base 25 and perimeter Find the area of a square whose diagonal is 50 inches. 6. Find the area of an isosceles triangle if one side is 6 and the other two sides are 5 units. 7. Area of a Kite. In the figure, AB is congruent to BC, AD is congruent to DC and BD is perpendicular to AC. Show that the area of ABCD = (1/2)(BD)(AC). B A E C D

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

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

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

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

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

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

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

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

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

Honors Geometry. Worksheet 4.1: Quadrilaterals. Quadrilateral:. (definition) Parallelogram:. (definition)

Honors Geometry. Worksheet 4.1: Quadrilaterals. Quadrilateral:. (definition) Parallelogram:. (definition) Honors Geometry Name: Worksheet 4.1: Quadrilaterals Fill in the blanks using definitions and theorems about quadrilaterals. Quadrilateral:. The midquad of a quadrilateral is a. The sum of the measures

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

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

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

Chapter 8. Quadrilaterals

Chapter 8. Quadrilaterals Chapter 8 Quadrilaterals 8.1 Find Angle Measures in Polygons Objective: Find angle measures in polygons. Essential Question: How do you find a missing angle measure in a convex polygon? 1) Any convex polygon.

More information

Polygons. Name each polygon Find the sum of the angle measures in each figure

Polygons. Name each polygon Find the sum of the angle measures in each figure Practice A Polygons Name each polygon. 1. 2. 3. Find the sum of the angle measures in each figure. 4. 5. 6. 7. 8. 9. Find the angle measures in each regular polygon. 10. 11. 12. 13. 14. 15. Give all the

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

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

Pre-AICE 2: Unit 5 Exam - Study Guide

Pre-AICE 2: Unit 5 Exam - Study Guide Pre-AICE 2: Unit 5 Exam - Study Guide 1 Find the value of x. (The figure may not be drawn to scale.) A. 74 B. 108 C. 49 D. 51 2 Find the measure of an interior angle and an exterior angle of a regular

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

Period: Date Lesson 13: Analytic Proofs of Theorems Previously Proved by Synthetic Means

Period: Date Lesson 13: Analytic Proofs of Theorems Previously Proved by Synthetic Means : Analytic Proofs of Theorems Previously Proved by Synthetic Means Learning Targets Using coordinates, I can find the intersection of the medians of a triangle that meet at a point that is two-thirds of

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

Unit 2: Triangles and Polygons

Unit 2: Triangles and Polygons Unit 2: Triangles and Polygons Background for Standard G.CO.9: Prove theorems about lines and angles. Objective: By the end of class, I should Using the diagram below, answer the following questions. Line

More information

Areas of Triangles and Quadrilaterals. Mrs. Poland January 5, 2010

Areas of Triangles and Quadrilaterals. Mrs. Poland January 5, 2010 Areas of Triangles and Quadrilaterals Mrs. Poland January 5, 2010 Review 1! A polygon with 7 sides is called a. A) nonagon B) dodecagon C) heptagon D) hexagon E) decagon Review 2! Find m

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

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 9: Coordinate Proof - Quadrilaterals Learning Targets

Lesson 9: Coordinate Proof - Quadrilaterals Learning Targets Lesson 9: Coordinate Proof - Quadrilaterals Learning Targets Using coordinates, I can find the intersection of the medians of a triangle that meet at a point that is two-thirds of the way along each median

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

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

5.6notes November 13, Based on work from pages , complete In an isosceles triangle, the &

5.6notes November 13, Based on work from pages , complete In an isosceles triangle, the & chapter 5 Based on work from pages 178-179, complete In an isosceles triangle, the & & & drawn from the vertex angle of an isosceles triangle are the! 5.1 Indirect proof. G: DB AC F is the midpt. of AC

More information

pd 3notes 5.4 November 09, 2016 Based on work from pages , complete In an isosceles triangle, the &

pd 3notes 5.4 November 09, 2016 Based on work from pages , complete In an isosceles triangle, the & chapter 5 Based on work from pages 178-179, complete In an isosceles triangle, the & & & drawn from the vertex angle of an isosceles triangle are the! 5.1 Indirect proof. G: DB AC F is the midpt. of AC

More information

Unit 5: Polygons and Quadrilaterals

Unit 5: Polygons and Quadrilaterals Unit 5: Polygons and Quadrilaterals Scale for Unit 5 4 Through independent work beyond what was taught in class, students could (examples include, but are not limited to): - Research a unique building

More information

Contents. Lines, angles and polygons: Parallel lines and angles. Triangles. Quadrilaterals. Angles in polygons. Congruence.

Contents. Lines, angles and polygons: Parallel lines and angles. Triangles. Quadrilaterals. Angles in polygons. Congruence. Colegio Herma. Maths Bilingual Departament Isabel Martos Martínez. 2015 Contents Lines, angles and polygons: Parallel lines and angles Triangles Quadrilaterals Angles in polygons Congruence Similarity

More information

Squares and Rectangles

Squares and Rectangles LESSON.1 Assignment Name Date Squares and Rectangles Properties of Squares and Rectangles 1. In quadrilateral VWXY, segments VX and WY bisect each other, and are perpendicular and congruent. Is this enough

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

Contents. Lines, angles and polygons: Parallel lines and angles. Triangles. Quadrilaterals. Angles in polygons. Congruence.

Contents. Lines, angles and polygons: Parallel lines and angles. Triangles. Quadrilaterals. Angles in polygons. Congruence. Colegio Herma. Maths Bilingual Departament Isabel Martos Martínez. 2015 Contents Lines, angles and polygons: Parallel lines and angles Triangles Quadrilaterals Angles in polygons Congruence Similarity

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

A. 180 B. 108 C. 360 D. 540

A. 180 B. 108 C. 360 D. 540 Part I - Multiple Choice - Circle your answer: REVIEW FOR FINAL EXAM - GEOMETRY 2 1. Find the area of the shaded sector. Q O 8 P A. 2 π B. 4 π C. 8 π D. 16 π 2. An octagon has sides. A. five B. six C.

More information

Name Date Class. The Polygon Angle Sum Theorem states that the sum of the interior angle measures of a convex polygon with n sides is (n 2)180.

Name Date Class. The Polygon Angle Sum Theorem states that the sum of the interior angle measures of a convex polygon with n sides is (n 2)180. Name Date Class 6-1 Properties and Attributes of Polygons continued The Polygon Angle Sum Theorem states that the sum of the interior angle measures of a convex polygon with n sides is (n 2)180. Convex

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

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

Q3 Exam Review Date: Per:

Q3 Exam Review Date: Per: Geometry Name: Q3 Exam Review Date: Per: Show all your work. Box or circle your final answer. When appropriate, write your answers in simplest radical form, as a simplified improper fraction, AND as a

More information

GEOMETRY COORDINATE GEOMETRY Proofs

GEOMETRY COORDINATE GEOMETRY Proofs GEOMETRY COORDINATE GEOMETRY Proofs Name Period 1 Coordinate Proof Help Page Formulas Slope: Distance: To show segments are congruent: Use the distance formula to find the length of the sides and show

More information

Answer Key. 1.1 The Three Dimensions. Chapter 1 Basics of Geometry. CK-12 Geometry Honors Concepts 1. Answers

Answer Key. 1.1 The Three Dimensions. Chapter 1 Basics of Geometry. CK-12 Geometry Honors Concepts 1. Answers 1.1 The Three Dimensions 1. Possible answer: You need only one number to describe the location of a point on a line. You need two numbers to describe the location of a point on a plane. 2. vary. Possible

More information

Chapter 6: Quadrilaterals. of a polygon is a segment that connects any two nonconsecutive. Triangle Quadrilateral Pentagon Hexagon

Chapter 6: Quadrilaterals. of a polygon is a segment that connects any two nonconsecutive. Triangle Quadrilateral Pentagon Hexagon Lesson 6-1: Angles of Polygons A vertices. Example: Date: of a polygon is a segment that connects any two nonconsecutive Triangle Quadrilateral Pentagon Hexagon Since the sum of the angle measures of a

More information

Polygon Interior Angles

Polygon Interior Angles Polygons can be named by the number of sides. A regular polygon has All other polygons are irregular. A concave polygon has All other polygons are convex, with all vertices facing outwards. Name each polygon

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

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

9.2. Polygons. Copyright 2005 Pearson Education, Inc.

9.2. Polygons. Copyright 2005 Pearson Education, Inc. 9.2 Polygons Polygons Polygons are names according to their number of sides. Number of Sides Name Number of Sides Name 3 Triangle 8 Octagon 4 Quadrilateral 9 Nonagon 5 Pentagon 10 Decagon 6 Hexagon 12

More information

22. A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel.

22. A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel. Chapter 4 Quadrilaterals 4.1 Properties of a Parallelogram Definitions 22. A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel. 23. An altitude of a parallelogram is the

More information

6-1 Study Guide and Intervention Angles of Polygons

6-1 Study Guide and Intervention Angles of Polygons 6-1 Study Guide and Intervention Angles of Polygons Polygon Interior Angles Sum The segments that connect the nonconsecutive vertices of a polygon are called diagonals. Drawing all of the diagonals from

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

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

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

1. AREAS. Geometry 199. A. Rectangle = base altitude = bh. B. Parallelogram = base altitude = bh. C. Rhombus = 1 product of the diagonals = 1 dd

1. AREAS. Geometry 199. A. Rectangle = base altitude = bh. B. Parallelogram = base altitude = bh. C. Rhombus = 1 product of the diagonals = 1 dd Geometry 199 1. AREAS A. Rectangle = base altitude = bh Area = 40 B. Parallelogram = base altitude = bh Area = 40 Notice that the altitude is different from the side. It is always shorter than the second

More information

1. Write three things you already know about angles. Share your work with a classmate. Does your classmate understand what you wrote?

1. Write three things you already know about angles. Share your work with a classmate. Does your classmate understand what you wrote? LESSON : PAPER FOLDING. Write three things you already know about angles. Share your work with a classmate. Does your classmate understand what you wrote? 2. Write your wonderings about angles. Share your

More information

Parallelograms. MA 341 Topics in Geometry Lecture 05

Parallelograms. MA 341 Topics in Geometry Lecture 05 Parallelograms MA 341 Topics in Geometry Lecture 05 Definitions A quadrilateral is a polygon with 4 distinct sides and four vertices. Is there a more precise definition? P 1 P 2 P 3 09-Sept-2011 MA 341

More information

Understanding Quadrilaterals

Understanding Quadrilaterals Understanding Quadrilaterals Parallelogram: A quadrilateral with each pair of opposite sides parallel. Properties: (1) Opposite sides are equal. (2) Opposite angles are equal. (3) Diagonals bisect one

More information

Formal Geometry UNIT 6 - Quadrilaterals

Formal Geometry UNIT 6 - Quadrilaterals Formal Geometry UNIT 6 - Quadrilaterals 14-Jan 15-Jan 16-Jan 17-Jan 18-Jan Day 1 Day Day 4 Kites and Day 3 Polygon Basics Trapezoids Proving Parallelograms Day 5 Homefun: Parallelograms Pg 48 431 #1 19,

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

Unit 5 Test Date Block

Unit 5 Test Date Block Geometry B Name Unit 5 Test Date Block 60 ANSWERS Directions: This test is written to cover Unit 5. Please answer each question to the best of your ability. If multiple steps are required, it is expected

More information

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

1. Take out a piece of notebook paper and make a hot dog fold over from the right side over to the pink line. Foldable

1. Take out a piece of notebook paper and make a hot dog fold over from the right side over to the pink line. Foldable Four sided polygon 1. Take out a piece of notebook paper and make a hot dog fold over from the right side over to the pink line. Foldable Foldable The fold crease 2. Now, divide the right hand section

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 9: Quadrilaterals

Unit 9: Quadrilaterals Unit 9: Quadrilaterals Topic/Assignment I CAN statement Turned in? Properties of Quadrilaterals HW: Worksheet Properties of all Quadrilaterals Properties of Parallelograms HW: Properties of Parallelograms

More information

Chapter 1-3 Parallel Lines, Vocab, and Linear Equations Review

Chapter 1-3 Parallel Lines, Vocab, and Linear Equations Review Geometry H Final Exam Review Chapter 1-3 Parallel Lines, Vocab, and Linear Equations Review 1. Use the figure at the right to answer the following questions. a. How many planes are there in the figure?

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

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

3. The sides of a rectangle are in ratio fo 3:5 and the rectangle s area is 135m2. Find the dimensions of the rectangle.

3. The sides of a rectangle are in ratio fo 3:5 and the rectangle s area is 135m2. Find the dimensions of the rectangle. Geometry B Honors Chapter Practice Test 1. Find the area of a square whose diagonal is. 7. Find the area of the triangle. 60 o 12 2. Each rectangle garden below has an area of 0. 8. Find the area of the

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

Name: Date: Period: Lab: Inscribed Quadrilaterals

Name: Date: Period: Lab: Inscribed Quadrilaterals Name: Date: Period: Materials: ompass Straightedge Lab: Inscribed Quadrilaterals Part A: Below are different categories of quadrilaterals. Each category has 2-4 figures. Using a compass and straightedge,

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

Problems #1. A convex pentagon has interior angles with measures (5x 12), (2x + 100), (4x + 16), (6x + 15), and (3x + 41). Find x.

Problems #1. A convex pentagon has interior angles with measures (5x 12), (2x + 100), (4x + 16), (6x + 15), and (3x + 41). Find x. 1 Pre-AP Geometry Chapter 10 Test Review Standards/Goals: G.CO.11/ C.1.i.: I can use properties of special quadrilaterals in a proof. D.2.g.: I can identify and classify quadrilaterals, including parallelograms,

More information

HIGH SCHOOL. Geometry. Soowook Lee

HIGH SCHOOL. Geometry. Soowook Lee HIGH SCHOOL Geometry Soowook Lee Chapter 4 Quadrilaterals This chapter will cover basic quadrilaterals, including parallelograms, trapezoids, rhombi, rectangles, squares, kites, and cyclic quadrilaterals.

More information

Quadrilaterals. Polygons Basics

Quadrilaterals. Polygons Basics Name: Quadrilaterals Polygons Basics Date: Objectives: SWBAT identify, name and describe polygons. SWBAT use the sum of the measures of the interior angles of a quadrilateral. A. The basics on POLYGONS

More information

3. Understanding Quadrilaterals

3. Understanding Quadrilaterals 3. Understanding Quadrilaterals Q 1 Name the regular polygon with 8 sides. Mark (1) Q 2 Find the number of diagonals in the figure given below. Mark (1) Q 3 Find x in the following figure. Mark (1) Q 4

More information

MATH 113 Section 8.2: Two-Dimensional Figures

MATH 113 Section 8.2: Two-Dimensional Figures MATH 113 Section 8.2: Two-Dimensional Figures Prof. Jonathan Duncan Walla Walla University Winter Quarter, 2008 Outline 1 Classifying Two-Dimensional Shapes 2 Polygons Triangles Quadrilaterals 3 Other

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

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

Polygons & Quadrilaterals Classwork

Polygons & Quadrilaterals Classwork Name: Class: Date: ID: A Polygons & Quadrilaterals Classwork Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The pentagon in the diagram below is formed

More information

6.1 What is a Polygon?

6.1 What is a Polygon? 6. What is a Polygon? Unit 6 Polygons and Quadrilaterals Regular polygon - Polygon Names: # sides Name 3 4 raw hexagon RPTOE 5 6 7 8 9 0 Name the vertices: Name the sides: Name the diagonals containing

More information

Review for Quadrilateral Test

Review for Quadrilateral Test Review for Quadrilateral Test 1. How many triangles are formed by drawing diagonals from one vertex in the figure? Find the sum of the measures of the angles in the figure. a. 6, 1080 b. 7, 1260 c. 7,

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

For all questions, E. NOTA means none of the above answers is correct. Diagrams are NOT drawn to scale.

For all questions, E. NOTA means none of the above answers is correct. Diagrams are NOT drawn to scale. For all questions, means none of the above answers is correct. Diagrams are NOT drawn to scale.. In the diagram, given m = 57, m = (x+ ), m = (4x 5). Find the degree measure of the smallest angle. 5. The

More information

Geometry Lesson 1 Introduction to Geometry (Grades 9-12) Instruction 1-5 Definitions of Figures

Geometry Lesson 1 Introduction to Geometry (Grades 9-12) Instruction 1-5 Definitions of Figures efinitions of igures Quadrilaterals Quadrilaterals are closed four-sided figures. The interior angles of a quadrilateral always total 360. Quadrilaterals classified in two groups: Trapeziums and Trapezoids.

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

Review Unit 5 t Find the measure of one interior angle in each regular polygon. Round your answer to the nearest tenth if necessary.

Review Unit 5 t Find the measure of one interior angle in each regular polygon. Round your answer to the nearest tenth if necessary. Worksheet by Kuta oftware LLC -1- Geometry Review nit 5 t Find the measure of one interior angle in each regular polygon. Round your answer to the nearest tenth if necessary. 1) 2) regular 18-gon Find

More information

NOTA" stands for none of these answers." Figures are not drawn to scale.

NOTA stands for none of these answers. Figures are not drawn to scale. NOTA" stands for none of these answers." Figures are not drawn to scale. 1. If Kyle does not do his homework, then he is lazy. Kyle is lazy. Which of the following must be true? a) Kyle never does his

More information

SOL Chapter Due Date

SOL Chapter Due Date Name: Block: Date: Geometry SOL Review SOL Chapter Due Date G.1 2.2-2.4 G.2 3.1-3.5 G.3 1.3, 4.8, 6.7, 9 G.4 N/A G.5 5.5 G.6 4.1-4.7 G.7 6.1-6.6 G.8 7.1-7.7 G.9 8.2-8.6 G.10 1.6, 8.1 G.11 10.1-10.6, 11.5,

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

Boardworks Ltd KS3 Mathematics. S1 Lines and Angles

Boardworks Ltd KS3 Mathematics. S1 Lines and Angles 1 KS3 Mathematics S1 Lines and Angles 2 Contents S1 Lines and angles S1.1 Labelling lines and angles S1.2 Parallel and perpendicular lines S1.3 Calculating angles S1.4 Angles in polygons 3 Lines In Mathematics,

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

Geometry Third Quarter Study Guide

Geometry Third Quarter Study Guide Geometry Third Quarter Study Guide 1. Write the if-then form, the converse, the inverse and the contrapositive for the given statement: All right angles are congruent. 2. Find the measures of angles A,

More information

Lesson 7.1. Angles of Polygons

Lesson 7.1. Angles of Polygons Lesson 7.1 Angles of Polygons Essential Question: How can I find the sum of the measures of the interior angles of a polygon? Polygon A plane figure made of three or more segments (sides). Each side intersects

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

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. 11-3 Objectives You will learn to: You will learn to find the area of a regular polygon. Vocabulary Center of a regular polygon Apothem

More information

theorems & postulates & stuff (mr. ko)

theorems & postulates & stuff (mr. ko) theorems & postulates & stuff (mr. ko) postulates 1 ruler postulate The points on a line can be matched one to one with the real numbers. The real number that corresponds to a point is the coordinate of

More information

Geometry First Semester Practice Final (cont)

Geometry First Semester Practice Final (cont) 49. Determine the width of the river, AE, if A. 6.6 yards. 10 yards C. 12.8 yards D. 15 yards Geometry First Semester Practice Final (cont) 50. In the similar triangles shown below, what is the value of

More information

NAME DATE PERIOD. A#1: Angles of Polygons

NAME DATE PERIOD. A#1: Angles of Polygons NAME DATE PERIOD A#1: Angles of Polygons Angle Sum of a Regular or Irregular Polygon Interior Angles Exterior Angles One Angle Measure of a Regular Polygon Find the sum of the measures of the interior

More information

Student Name: Teacher: Date: Miami-Dade County Public Schools. Test: 9_12 Mathematics Geometry Exam 2

Student Name: Teacher: Date: Miami-Dade County Public Schools. Test: 9_12 Mathematics Geometry Exam 2 Student Name: Teacher: Date: District: Miami-Dade County Public Schools Test: 9_12 Mathematics Geometry Exam 2 Description: GEO Topic 5: Quadrilaterals and Coordinate Geometry Form: 201 1. If the quadrilateral

More information