THEOREM 8.1. Polygon Interior Angles Theorem. interior angles of a convex polygon with n sides is (n 2)p180.

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "THEOREM 8.1. Polygon Interior Angles Theorem. interior angles of a convex polygon with n sides is (n 2)p180."

Transcription

1 Page of 7 8. ngles in Polygons Goal Find the measures of interior and exterior angles of polygons. The definitions for interior angles and exterior angles can be extended to include angles formed in any polygon. In the diagrams shown below, interior angles are red, and exterior angles are blue. Key Words interior angle p. 8 exterior angle p. 8 interior angles exterior angles ctivity 8. suggests the Polygon Interior ngles Theorem shown below. THORM 8. Polygon Interior ngles Theorem Words The sum of the measures of the interior angles of a convex polygon with n sides is (n )p80. Symbols ma ma... man (n )p80 6 n 6 XMPL Use the Polygon Interior ngles Theorem Find the sum of the measures of the interior angles of a convex heptagon. heptagon has 7 sides. Use the Polygon Interior ngles Theorem and substitute 7 for n. (n )p80 (7 )p80 Substitute 7 for n. p Simplify. Multiply. NSWR The sum of the measures of the interior angles of a convex heptagon is ngles in Polygons 7

2 Page of 7 XMPL Find the measure of a in the diagram. Find the Measure of an Interior ngle The polygon has 6 sides, so the sum of the measures of the interior angles is: (n )p80 (6 )p80 p F Student Help SKILLS RVIW To review solving an equation, see p. 67. dd the measures of the interior angles and set the sum equal to ma 70 The sum is ma 70 Simplify. ma Subtract 607. NSWR The measure of a is. XMPL Find the measure of an interior angle of a regular octagon. The sum of the measures of the interior angles of any octagon is: (n )p80 (8 )p80 6p ecause the octagon is regular, each angle has the same measure. So, divide 080 by 8 to find the measure of one interior angle Interior ngles of a Regular Polygon NSWR The measure of an interior angle of a regular octagon is. Find Measures of Interior ngles In xercises, find the measure of ag.. F G. H. H J J G F 0 0 G 8 H L M K K. Find the measure of an interior angle of a regular polygon with twelve sides. 8 hapter 8 Polygons and rea

3 Page of 7 xterior ngles The diagrams below show that the sum of the measures of the exterior angles of the convex polygon is 60. Visualize It! circle contains two straight angles. So, there are 80 80, or 60, in a circle or 60 Shade one exterior ut out the rrange the exterior angle at each vertex. exterior angles. angles to form The sum of the measures of the exterior angles of a convex polygon does not depend on the number of sides that the polygon has. THORM 8. Polygon xterior ngles Theorem Words The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 60. Symbols ma ma... man 60 n XMPL Find the value of x. Find the Measure of an xterior ngle Using the Polygon xterior ngles Theorem, set the sum of the measures of the exterior angles equal to Polygon xterior ngles Theorem 80 x 60 ombine like terms. x 80 NSWR The value of x is Subtract 80 from each side. x 60 ivide each side by. 8. ngles in Polygons 9

4 Page of 7 Find xterior ngle Measures Find the value of x xercises Guided Practice Vocabulary heck. Name an interior angle and an exterior angle of polygon shown at the right. G Skill heck. Write the formula that is used to find the sum of the measures of the interior angles of any convex polygon with n sides. F H. Use your answer from xercise to find the sum of the measures of the interior angles of a convex polygon with 9 sides. Write an equation to find the measure of a. o not solve the equation hapter 8 Polygons and rea

5 Page of 7 Practice and pplications xtra Practice See p Sum of Interior ngle Measures Find the sum of the measures of the interior angles of the convex polygon Polygons with n Sides Find the sum of the measures of the interior angles of the convex polygon with n sides.. n 0. n. n 0. n 0. n 6. n 00 Interior ngle Measures Find the measure of a F F IStudent Help I L S S Z O N. O M HOMWORK HLP xtra help with problem solving in xs. is at classzone.com Interior ngles of Regular Polygons Find the measure of an interior angle of the regular polygon.... Using lgebra Find the value of x. Homework Help xample : xs. 8 6 xample : xs. 7 0 xample : xs. xample : xs., ngles in Polygons

6 Page 6 of 7 Sports aseball home plate for a baseball field is a pentagon as shown. 6. Is the polygon regular? xplain why or why not. 7. What is the sum of the interior angles? 8. Find the measures of a and a. SLL Home plate is used to find the placement of the foul lines on the playing field. Visualize It! ut a strip of lined paper and tie it into an overhand knot as shown. Gently flatten the knot to form a pentagon. The pentagon should be regular. 9. Find the measure of an interior angle of a regular pentagon. 0. Measure the interior angles of your knot with a protractor. Use your answer to xercise 9 to determine whether your pentagon is regular. Logical Reasoning Select the word that makes the statement true.. The sum of the measures of the exterior angles of a convex polygon, one at each vertex, is (always, sometimes, never) 60.. The sum of the measures of the interior angles of a convex octagon is (always, sometimes, never) 0.. The measures of the exterior angles of a convex polygon are (always, sometimes, never) equal.. Outdoor Furniture You are constructing a regular hexagonal wooden bench like the one shown. On the bench, a ca. Find the measures of a and a so that you know what angle to use to cut the pieces of wood. hallenge Find the number of sides of the regular polygon with the given exterior angle measure hapter 8 Polygons and rea

7 Page 7 of 7 Standardized Test Practice Multiple hoice In xercises 9 and 0, use the diagram below. 9. What is the value of x? What is the measure of ap? P P 0 0 U R S 0 T F 9 G 78 H 6 J Mixed Review Using a entroid is the centroid of T. Find and. (Lesson.6). 6.. lgebra Skills bsolute Value valuate. (Skills Review, p. 66) Quiz ecide whether the polygon is regular. xplain your answer. (Lesson 8.)... Find the measure of a. (Lesson 8.) ngles in Polygons

Goal Find angle measures in triangles. Key Words corollary. Student Help. Triangle Sum Theorem THEOREM 4.1. Words The sum of the measures of EXAMPLE

Goal Find angle measures in triangles. Key Words corollary. Student Help. Triangle Sum Theorem THEOREM 4.1. Words The sum of the measures of EXAMPLE Page of 6 4. ngle Measures of Triangles Goal Find angle measures in triangles. The diagram below shows that when you tear off the corners of any triangle, you can place the angles together to form a straight

More information

Lesson 6: Polygons and Angles

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

More information

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

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

More information

22.1 Interior and Exterior Angles

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

More information

4.7 Triangle Inequalities

4.7 Triangle Inequalities age 1 of 7 4.7 riangle Inequalities Goal Use triangle measurements to decide which side is longest and which angle is largest. he diagrams below show a relationship between the longest and shortest sides

More information

Angle Relationships in Parallel Lines and Triangles?

Angle Relationships in Parallel Lines and Triangles? ngle Relationships in Parallel Lines and Triangles? MOUL 11 LSSON 11.1 Parallel Lines ut by a Transversal OMMON OR SSNTIL QUSTION How can you use angle relationships in parallel lines and triangles to

More information

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

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

More information

A of a polygon is a segment that joins two nonconsecutive vertices. 1. How many degrees are in a triangle?

A 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 information

Rules of angles (7 9)

Rules 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 information

Which shapes make floor tilings?

Which shapes make floor tilings? Which shapes make floor tilings? Suppose you are trying to tile your bathroom floor. You are allowed to pick only one shape and size of tile. The tile has to be a regular polygon (meaning all the same

More information

Chapter 1 Exam. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question. 1.

Chapter 1 Exam. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Name: lass: ate: I: hapter 1 Exam Multiple hoice Identify the choice that best completes the statement or answers the question. 1. bisects, m = (7x 1), and m = (4x + 8). Find m. a. m = c. m = 40 b. m =

More information

Exterior Angles of Polygons

Exterior 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 information

Measure and classify angles. Identify and use congruent angles and the bisector of an angle. big is a degree? One of the first references to the

Measure and classify angles. Identify and use congruent angles and the bisector of an angle. big is a degree? One of the first references to the ngle Measure Vocabulary degree ray opposite rays angle sides vertex interior exterior right angle acute angle obtuse angle angle bisector tudy ip eading Math Opposite rays are also known as a straight

More information

Perimeter and Area of Similar Figures

Perimeter and Area of Similar Figures 11.3 erimeter and Area of Similar igures Before You used ratios to find perimeters of similar figures. Now You will use ratios to find areas of similar figures. Why So you can apply similarity in cooking,

More information

Chapter 3. Chapter 3 Opener. Section 3.1. Big Ideas Math Blue Worked-Out Solutions. Try It Yourself (p. 101) So, the value of x is 112.

Chapter 3. Chapter 3 Opener. Section 3.1. Big Ideas Math Blue Worked-Out 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 information

Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question. Name: lass: _ ate: _ I: SSS Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Given the lengths marked on the figure and that bisects E, use SSS to explain

More information

Geo - CH6 Practice Test

Geo - 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 information

Polygon Properties and Tiling

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

More information

Topic : Exterior Angles - Worksheet How many degrees are there in the sum of the exterior angles of a regular hexagon?

Topic : 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 information

LESSON PLAN #1: Discover a Relationship

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

More information

Intermediate Math Circles October 10, 2012 Geometry I: Angles

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

More information

Similar shapes. 33.1 Similar triangles CHAPTER. Example 1

Similar shapes. 33.1 Similar triangles CHAPTER. Example 1 imilar shapes 33 HTR 33.1 imilar triangles Triangle and triangle have the same shape but not the same size. They are called similar triangles. The angles in triangle are the same as the angles in triangle,

More information

Geometry Chapter 1 Review

Geometry Chapter 1 Review Name: lass: ate: I: Geometry hapter 1 Review Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Name two lines in the figure. a. and T c. W and R b. WR and

More information

For the circle above, EOB is a central angle. So is DOE. arc. The (degree) measure of ù DE is the measure of DOE.

For the circle above, EOB is a central angle. So is DOE. arc. The (degree) measure of ù DE is the measure of DOE. efinition: circle is the set of all points in a plane that are equidistant from a given point called the center of the circle. We use the symbol to represent a circle. The a line segment from the center

More information

pair of parallel sides. The parallel sides are the bases. The nonparallel sides are the legs.

pair of parallel sides. The parallel sides are the bases. The nonparallel sides are the legs. age 1 of 5 6.5 rapezoids Goal Use properties of trapezoids. trapezoid is a quadrilateral with eactly one pair of parallel sides. he parallel sides are the bases. he nonparallel sides are the legs. leg

More information

Geo - CH9 Practice Test

Geo - CH9 Practice Test Geo - H9 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Find the area of the parallelogram. a. 35 in 2 c. 21 in 2 b. 14 in 2 d. 28 in 2 2.

More information

Monomial. 5 1 x A sum is not a monomial. 2 A monomial cannot have a. x 21. degree. 2x 3 1 x 2 2 5x Rewrite a polynomial

Monomial. 5 1 x A sum is not a monomial. 2 A monomial cannot have a. x 21. degree. 2x 3 1 x 2 2 5x Rewrite a polynomial 9.1 Add and Subtract Polynomials Before You added and subtracted integers. Now You will add and subtract polynomials. Why? So you can model trends in recreation, as in Ex. 37. Key Vocabulary monomial degree

More information

UNIT H1 Angles and Symmetry Activities

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

More information

Dates, assignments, and quizzes subject to change without advance notice. Monday Tuesday Block Day Friday. 3 (only see 6 th, 4

Dates, assignments, and quizzes subject to change without advance notice. Monday Tuesday Block Day Friday. 3 (only see 6 th, 4 Name: Period GL UNIT 12: IRLS I can define, identify and illustrate the following terms: Interior of a circle hord xterior of a circle Secant of a circle Tangent to a circle Point of tangency entral angle

More information

Pre-AP Geometry 12-2 Study Guide: Arcs and Chords (pp 802-809) Page! 1 of! 12

Pre-AP Geometry 12-2 Study Guide: Arcs and Chords (pp 802-809) Page! 1 of! 12 Pre-P Geometry 12-2 Study Guide: rcs and hords (pp 802-809) Page! 1 of! 12 ttendance Problems 1. What percent of 60 is 18? 2. What number is 44% of 6? 3. Find! m!wvx. I can apply properties of arcs. I

More information

Geometry Progress Ladder

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

More information

Perimeter and Area. An artist uses perimeter and area to determine the amount of materials it takes to produce a piece such as this.

Perimeter 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 information

11.2 Chords & Central Angles Quiz

11.2 Chords & Central Angles Quiz Name: lass: ate: I: 11.2 hords & entral ngles Quiz Multiple hoice Identify the choice that best completes the statement or answers the question. 1. In the diagram below, circle O has a radius of 5, and

More information

Unit 8. Quadrilaterals. Academic Geometry Spring Name Teacher Period

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

More information

Unit 3: Triangle Bisectors and Quadrilaterals

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

More information

Evaluate and Simplify Algebraic Expressions

Evaluate and Simplify Algebraic Expressions 1.2 Evaluate and Simplify Algebraic Expressions Before You studied properties of real numbers. Now You will evaluate and simplify expressions involving real numbers. Why? So you can estimate calorie use,

More information

NAME DATE PERIOD. Study Guide and Intervention

NAME DATE PERIOD. Study Guide and Intervention opyright Glencoe/McGraw-Hill, a division of he McGraw-Hill ompanies, Inc. 5-1 M IO tudy Guide and Intervention isectors, Medians, and ltitudes erpendicular isectors and ngle isectors perpendicular bisector

More information

Hands-On Mini Lab. Step 2 Pick one vertex and draw a segment to the opposite vertex. The angles of a quadrilateral have a special relationship.

Hands-On Mini Lab. Step 2 Pick one vertex and draw a segment to the opposite vertex. The angles of a quadrilateral have a special relationship. 10-7 Quadrilaterals MAIN IDEA I will classify quadrilaterals and find missing angle measures in quadrilaterals. New Vocabulary quadrilateral rectangle square ogram trapezoid Hands-On Mini Lab The figure

More information

Inscribed Angle Theorem and Its Applications

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

More information

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

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

More information

Unit 3 Practice Test. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

Unit 3 Practice Test. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question. Name: lass: ate: I: Unit 3 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. The radius, diameter, or circumference of a circle is given. Find

More information

Fractions. Cavendish Community Primary School

Fractions. Cavendish Community Primary School Fractions Children in the Foundation Stage should be introduced to the concept of halves and quarters through play and practical activities in preparation for calculation at Key Stage One. Y Understand

More information

Prove Triangles Congruent by ASA and AAS

Prove Triangles Congruent by ASA and AAS 4.5 rove Triangles ongruent by S and S efore ou used the SSS, SS, and H congruence methods. Now ou will use two more methods to prove congruences. hy So you can recognize congruent triangles in bikes,

More information

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

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

More information

Tons of Free Math Worksheets at:

Tons 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 information

1.7 Find Perimeter, Circumference,

1.7 Find Perimeter, Circumference, .7 Find Perimeter, Circumference, and rea Goal p Find dimensions of polygons. Your Notes FORMULS FOR PERIMETER P, RE, ND CIRCUMFERENCE C Square Rectangle side length s length l and width w P 5 P 5 s 5

More information

Geometry Notes Chapter 12. Name: Period:

Geometry Notes Chapter 12. Name: Period: Geometry Notes Chapter 1 Name: Period: Vocabulary Match each term on the left with a definition on the right. 1. image A. a mapping of a figure from its original position to a new position. preimage B.

More information

Lesson 21. Chapter 2: Perimeter, Area & Volume. Lengths and Areas of Rectangles, Triangles and Composite Shapes

Lesson 21. Chapter 2: Perimeter, Area & Volume. Lengths and Areas of Rectangles, Triangles and Composite Shapes ourse: HV Lesson hapter : Perimeter, rea & Volume Lengths and reas of Rectangles, Triangles and omposite Shapes The perimeter of a shape is the total length of its boundary. You can find the perimeter

More information

Parallel and Perpendicular. We show a small box in one of the angles to show that the lines are perpendicular.

Parallel and Perpendicular. We show a small box in one of the angles to show that the lines are perpendicular. CONDENSED L E S S O N. Parallel and Perpendicular In this lesson you will learn the meaning of parallel and perpendicular discover how the slopes of parallel and perpendicular lines are related use slopes

More information

1.2 Inductive Reasoning

1.2 Inductive Reasoning Page 1 of 6 1.2 Inductive Reasoning Goal Use inductive reasoning to make conjectures. Key Words conjecture inductive reasoning counterexample Scientists and mathematicians look for patterns and try to

More information

2.1. Inductive Reasoning EXAMPLE A

2.1. Inductive Reasoning EXAMPLE A CONDENSED LESSON 2.1 Inductive Reasoning In this lesson you will Learn how inductive reasoning is used in science and mathematics Use inductive reasoning to make conjectures about sequences of numbers

More information

Year 10 Term 1 Homework

Year 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 information

Shapes & Designs Notes

Shapes & Designs Notes Problem 1.1 Definitions: regular polygons - polygons in which all the side lengths and angles have the same measure edge - also referred to as the side of a figure tiling - covering a flat surface with

More information

Angle Vocabulary, Complementary & Supplementary Angles

Angle Vocabulary, Complementary & Supplementary Angles ngle Vocabulary, omplementary & Supplementary ngles Review 1 1. What is the definition of an acute angle? 2. Name the angle shown. 3. What is the definition of complimentary angles? 4. What is the definition

More information

This is a tentative schedule, date may change. Please be sure to write down homework assignments daily.

This is a tentative schedule, date may change. Please be sure to write down homework assignments daily. Mon Tue Wed Thu Fri Aug 26 Aug 27 Aug 28 Aug 29 Aug 30 Introductions, Expectations, Course Outline and Carnegie Review summer packet Topic: (1-1) Points, Lines, & Planes Topic: (1-2) Segment Measure Quiz

More information

Possible Stage Two Mathematics Test Topics

Possible Stage Two Mathematics Test Topics Possible Stage Two Mathematics Test Topics The Stage Two Mathematics Test questions are designed to be answerable by a good problem-solver with a strong mathematics background. It is based mainly on material

More information

Target To know the properties of a rectangle

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

More information

Geometry Chapter 9 Extending Perimeter, Circumference, and Area

Geometry Chapter 9 Extending Perimeter, Circumference, and Area Geometry Chapter 9 Extending Perimeter, Circumference, and Area Lesson 1 Developing Formulas for Triangles and Quadrilaterals Learning Target (LT-1) Solve problems involving the perimeter and area of triangles

More information

MA.7.G.4.2 Predict the results of transformations and draw transformed figures with and without the coordinate plane.

MA.7.G.4.2 Predict the results of transformations and draw transformed figures with and without the coordinate plane. MA.7.G.4.2 Predict the results of transformations and draw transformed figures with and without the coordinate plane. Symmetry When you can fold a figure in half, with both sides congruent, the fold line

More information

11.3 Curves, Polygons and Symmetry

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

More information

of surface, 569-571, 576-577, 578-581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433

of surface, 569-571, 576-577, 578-581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433 Absolute Value and arithmetic, 730-733 defined, 730 Acute angle, 477 Acute triangle, 497 Addend, 12 Addition associative property of, (see Commutative Property) carrying in, 11, 92 commutative property

More information

GAP CLOSING. 2D Measurement. Intermediate / Senior Student Book

GAP CLOSING. 2D Measurement. Intermediate / Senior Student Book GAP CLOSING 2D Measurement Intermediate / Senior Student Book 2-D Measurement Diagnostic...3 Areas of Parallelograms, Triangles, and Trapezoids...6 Areas of Composite Shapes...14 Circumferences and Areas

More information

Areas of Circles and Sectors. GO for Help

Areas of Circles and Sectors. GO for Help -7 What You ll Learn To find the areas of circles, sectors, and segments of circles... nd Why To compare the area of different-size pizzas, as in Example reas of ircles and Sectors heck Skills You ll Need

More information

Lesson 1: Introducing Circles

Lesson 1: Introducing Circles IRLES N VOLUME Lesson 1: Introducing ircles ommon ore Georgia Performance Standards M9 12.G..1 M9 12.G..2 Essential Questions 1. Why are all circles similar? 2. What are the relationships among inscribed

More information

Intermediate Math Competition series (IM), Session 2, day 1, IDEA MATH Lexington, Massachusetts 1. Special angles

Intermediate Math Competition series (IM), Session 2, day 1, IDEA MATH Lexington, Massachusetts 1. Special angles Intermediate Math ompetition series (IM), Session 2, day 1, I MTH Lexington, Massachusetts 1 Special angles Zuming Feng hillips xeter cademy zfeng@exeter.edu Sentry theorem xample 1.1. lex walks along

More information

11-4 Areas of Regular Polygons and Composite Figures

11-4 Areas of Regular Polygons and Composite Figures 1. In the figure, square ABDC is inscribed in F. Identify the center, a radius, an apothem, and a central angle of the polygon. Then find the measure of a central angle. Center: point F, radius:, apothem:,

More information

ASA Angle Side Angle SAA Side Angle Angle SSA Side Side Angle. B a C

ASA Angle Side Angle SAA Side Angle Angle SSA Side Side Angle. B a C 8.2 The Law of Sines Section 8.2 Notes Page 1 The law of sines is used to solve for missing sides or angles of triangles when we have the following three cases: S ngle Side ngle S Side ngle ngle SS Side

More information

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

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

More information

Pre-Algebra 2008. Academic Content Standards Grade Eight Ohio. Number, Number Sense and Operations Standard. Number and Number Systems

Pre-Algebra 2008. Academic Content Standards Grade Eight Ohio. Number, Number Sense and Operations Standard. Number and Number Systems Academic Content Standards Grade Eight Ohio Pre-Algebra 2008 STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express large numbers and small

More information

11-1 Lines that Intersect Circles Quiz

11-1 Lines that Intersect Circles Quiz Name: lass: ate: I: 11-1 Lines that Intersect ircles Quiz Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Identify the secant that intersects ñ. a. c. b.

More information

Geometry Chapter 9 Extending Perimeter, Circumference, and Area

Geometry Chapter 9 Extending Perimeter, Circumference, and Area Geometry Chapter 9 Extending Perimeter, Circumference, and Area Lesson 1 Developing Formulas for Triangles and Quadrilaterals Learning Targets LT9-1: Solve problems involving the perimeter and area of

More information

MATH STUDENT BOOK. 8th Grade Unit 6

MATH STUDENT BOOK. 8th Grade Unit 6 MATH STUDENT BOOK 8th Grade Unit 6 Unit 6 Measurement Math 806 Measurement Introduction 3 1. Angle Measures and Circles 5 Classify and Measure Angles 5 Perpendicular and Parallel Lines, Part 1 12 Perpendicular

More information

ACTIVITY: Multiplying Binomials Using Algebra Tiles. Work with a partner. Six different algebra tiles are shown below.

ACTIVITY: Multiplying Binomials Using Algebra Tiles. Work with a partner. Six different algebra tiles are shown below. 7.3 Multiplying Polynomials How can you multiply two binomials? 1 ACTIVITY: Multiplying Binomials Using Algebra Tiles Work with a partner. Six different algebra tiles are shown below. 1 1 x x x x Write

More information

1.6. Solve Linear Inequalities E XAMPLE 1 E XAMPLE 2. Graph simple inequalities. Graph compound inequalities

1.6. Solve Linear Inequalities E XAMPLE 1 E XAMPLE 2. Graph simple inequalities. Graph compound inequalities .6 Solve Linear Inequalities Before You solved linear equations. Now You will solve linear inequalities. Why? So you can describe temperature ranges, as in Ex. 54. Key Vocabulary linear inequality compound

More information

Volume of Spheres. A geometric plane passing through the center of a sphere divides it into. into the Northern Hemisphere and the Southern Hemisphere.

Volume of Spheres. A geometric plane passing through the center of a sphere divides it into. into the Northern Hemisphere and the Southern Hemisphere. Page 1 of 7 9.6 Surface Area and Volume of Spheres Goal Find surface areas and volumes of spheres. Key Words sphere hemisphere A globe is an example of a sphere. A sphere is the set of all points in space

More information

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

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

More information

Area of Trapezoids. Find the area of the trapezoid. 7 m. 11 m. 2 Use the Area of a Trapezoid. Find the value of b 2

Area of Trapezoids. Find the area of the trapezoid. 7 m. 11 m. 2 Use the Area of a Trapezoid. Find the value of b 2 Page 1 of. Area of Trapezoids Goal Find te area of trapezoids. Recall tat te parallel sides of a trapezoid are called te bases of te trapezoid, wit lengts denoted by and. base, eigt Key Words trapezoid

More information

Geometry 8-1 Angles of Polygons

Geometry 8-1 Angles of Polygons . Sum of Measures of Interior ngles Geometry 8-1 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 information

Integrated Algebra: Geometry

Integrated Algebra: Geometry Integrated Algebra: Geometry Topics of Study: o Perimeter and Circumference o Area Shaded Area Composite Area o Volume o Surface Area o Relative Error Links to Useful Websites & Videos: o Perimeter and

More information

56 questions (multiple choice, check all that apply, and fill in the blank) The exam is worth 224 points.

56 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 information

Signs, Signs, Every Place There Are Signs! Area of Regular Polygons p. 171 Boundary Lines Area of Parallelograms and Triangles p.

Signs, Signs, Every Place There Are Signs! Area of Regular Polygons p. 171 Boundary Lines Area of Parallelograms and Triangles p. C H A P T E R Perimeter and Area Regatta is another word for boat race. In sailing regattas, sailboats compete on courses defined by marks or buoys. These courses often start and end at the same mark,

More information

A discus thrower spins around in a circle one and a half times, then releases the discus. The discus forms a path tangent to the circle.

A discus thrower spins around in a circle one and a half times, then releases the discus. The discus forms a path tangent to the circle. Page 1 of 6 11.2 Popeties of Tangents Goal Use popeties of a tangent to a cicle. Key Wods point of tangency p. 589 pependicula p. 108 tangent segment discus thowe spins aound in a cicle one and a half

More information

EXPECTED BACKGROUND KNOWLEDGE

EXPECTED BACKGROUND KNOWLEDGE MOUL - 3 oncurrent Lines 12 ONURRNT LINS You have already learnt about concurrent lines, in the lesson on lines and angles. You have also studied about triangles and some special lines, i.e., medians,

More information

10.2 45-45 -90 Triangles

10.2 45-45 -90 Triangles Page of 6 0. --0 Triangles Goal Find the side lengths of --0 triangles. Key Words --0 triangle isosceles triangle p. 7 leg of a right triangle p. hypotenuse p. Geo-Activity Eploring an Isosceles Right

More information

Business Statistics & Presentation of Data BASIC MATHEMATHICS MATH0101

Business Statistics & Presentation of Data BASIC MATHEMATHICS MATH0101 Business Statistics & Presentation of Data BASIC MATHEMATHICS MATH0101 1 STATISTICS??? Numerical facts eg. the number of people living in a certain town, or the number of cars using a traffic route each

More information

INFORMATION FOR PARENTS AND CARERS TARGETS IN MATHEMATICS

INFORMATION FOR PARENTS AND CARERS TARGETS IN MATHEMATICS Emerging towards the expected Year 1 level I can share 6 objects between 2 children. I can write and use numbers (less than 10) in role play. I can compare bigger than and smaller than in role play. I

More information

Unknown Angle Problems with Inscribed Angles in Circles

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

More information

Geometry Chapter 10 Study Guide Name

Geometry Chapter 10 Study Guide Name eometry hapter 10 Study uide Name Terms and Vocabulary: ill in the blank and illustrate. 1. circle is defined as the set of all points in a plane that are equidistant from a fixed point called the center.

More information

The area of a figure is the measure of the size of the region enclosed by the figure. Formulas for the area of common figures: square: A = s 2

The area of a figure is the measure of the size of the region enclosed by the figure. Formulas for the area of common figures: square: A = s 2 The area of a figure is the measure of the size of the region enclosed by the figure. Formulas for the area of common figures: square: A = s 2 s s rectangle: A = l w parallelogram: A = b h h b triangle:

More information

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

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

More information

Year 9 mathematics test

Year 9 mathematics test Ma KEY STAGE 3 Year 9 mathematics test Tier 6 8 Paper 1 Calculator not allowed First name Last name Class Date Please read this page, but do not open your booklet until your teacher tells you to start.

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 Essential Question: When do we need standard symbols, operations, and rules in mathematics? (CAIU)

Unit Essential Question: When do we need standard symbols, operations, and rules in mathematics? (CAIU) Page 1 Whole Numbers Unit Essential : When do we need standard symbols, operations, and rules in mathematics? (CAIU) M6.A.3.2.1 Whole Number Operations Dividing with one digit (showing three forms of answers)

More information

Geometry Unit 6 Areas and Perimeters

Geometry Unit 6 Areas and Perimeters Geometry Unit 6 Areas and Perimeters Name Lesson 8.1: Areas of Rectangle (and Square) and Parallelograms How do we measure areas? Area is measured in square units. The type of the square unit you choose

More information

Level 1. AfL Questions for assessing Strand Five : Understanding Shape. NC Level Objectives AfL questions from RF

Level 1. AfL Questions for assessing Strand Five : Understanding Shape. NC Level Objectives AfL questions from RF AfL Questions for assessing Strand Five : Understanding Shape NC Level Objectives AfL questions from RF Level 1 I can use language such as circle or bigger to describe the shape and size of solids and

More information

Quadrilaterals Unit Review

Quadrilaterals Unit Review Name: Class: Date: Quadrilaterals Unit Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. ( points) In which polygon does the sum of the measures of

More information

Geometry Review. Here are some formulas and concepts that you will need to review before working on the practice exam.

Geometry Review. Here are some formulas and concepts that you will need to review before working on the practice exam. Geometry Review Here are some formulas and concepts that you will need to review before working on the practice eam. Triangles o Perimeter or the distance around the triangle is found by adding all of

More information

Applications for Triangles

Applications for Triangles Not drawn to scale Applications for Triangles 1. 36 in. 40 in. 33 in. 1188 in. 2 69 in. 2 138 in. 2 1440 in. 2 2. 188 in. 2 278 in. 2 322 in. 2 none of these Find the area of a parallelogram with the given

More information

Grade 6 Angle size. Required close-to-at-hand prior knowledge: Knowing what angles look like. Understanding what a rotation is.

Grade 6 Angle size. Required close-to-at-hand prior knowledge: Knowing what angles look like. Understanding what a rotation is. Grade 6 Angle size 6.SS.1 Demonstrate an understanding of angles by identifying examples of angles in the environment classifying angles according to their measure estimating the measure of angles using

More information

Incenter and Circumcenter Quiz

Incenter and Circumcenter Quiz Name: lass: ate: I: Incenter and ircumcenter Quiz Multiple hoice Identify the choice that best completes the statement or answers the question.. The diagram below shows the construction of the center of

More information