1.7 Find Perimeter, Circumference,

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "1.7 Find Perimeter, Circumference,"

Transcription

1 .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 5 Triangle Circle side lengths a, b, radius r a c and c, base b, h C 5 and height h. 5 P 5 5 b Pi (π) is the ratio of a circle's circumference to its diameter. r w Example Find the perimeter and area of a rectangle Tennis The in-bounds portion of a singles tennis court is shown. Find its perimeter and area. Perimeter rea P 5 2l 2w 5 lw 5 2( ) 2( ) 5 ( ) 5 5 The perimeter is ft and the area is ft ft 78 ft Checkpoint Complete the following exercise.. In Example, the width of the in-bounds rectangle increases to 36 feet for doubles play. Find the perimeter and area of the in-bounds rectangle. 24 Lesson.7 Geometry Notetaking Guide Copyright Holt McDougal. ll rights reserved.

2 .7 Find Perimeter, Circumference, and rea Goal p Find dimensions of polygons. Your Notes FORMULS FOR PERIMETER P, RE, ND CIRCUMFERENCE C Square side length s P 5 4s 5 s 2 s Rectangle length l and width w P 5 2l 2w 5 lw Triangle Circle side lengths a, b, radius r a c and c, base b, h C 5 2πr and height h. 5 πr 2 P 5 a b c b Pi (π) is the ratio of a 5 } 2 bh circle's circumference to its diameter. r w Example Find the perimeter and area of a rectangle Tennis The in-bounds portion of a singles tennis court is shown. Find its perimeter and area. Perimeter rea P 5 2l 2w 5 lw 5 2( 78 ) 2( 27 ) 5 78 ( 27 ) The perimeter is 20 ft and the area is 206 ft ft 78 ft Checkpoint Complete the following exercise.. In Example, the width of the in-bounds rectangle increases to 36 feet for doubles play. Find the perimeter and area of the in-bounds rectangle. perimeter: 228 ft, area: 2808 ft 2 24 Lesson.7 Geometry Notetaking Guide Copyright Holt McDougal. ll rights reserved.

3 Your Notes The approximations 3.4 and } 22 7 are commonly used as approximations for the irrational number π. Unless told otherwise, use 3.4 for π. Example 2 rchery The smallest circle on an Olympic target is 2 centimeters in diameter. Find the approximate circumference and area of the smallest circle. First find the radius. The diameter is 2 centimeters, so the radius is } 2 ( ) 5 centimeters. Then find the circumference and area. Use 3.4 for π. P 5 2πr ø 2( )( ) 5 5 πr 2 ø ( ) 2 5 Find the circumference and area of a circle Checkpoint Find the approximate circumference and area of the circle m Example 3 Using a coordinate plane Triangle JKL has vertices J(, 6), K(6, 6), and L(3, 2). Find the approximate perimeter of triangle JKL. Write down your calculations to make sure you do not make a mistake substituting values in the Distance Formula. First draw triangle JKL in a coordinate plane. Then find the side lengths. ecause } JK is horizontal, use the to find JK. Use the to find JL and LK. JK units JL 5 Ï }}} ( 2 ) 2 (2 2 ) 2 5 Ï } ø units LK 5 Ï }}} ( 2 3) 2 ( 2 2) 2 5 Ï } 5 units Then find the perimeter. P 5 JK JL LK ø 5 units. y x Copyright Holt McDougal. ll rights reserved. Lesson.7 Geometry Notetaking Guide 25

4 Your Notes The approximations 3.4 and } 22 7 are commonly used as approximations for the irrational number π. Unless told otherwise, use 3.4 for π. Example 2 Find the circumference and area of a circle rchery The smallest circle on an Olympic target is 2 centimeters in diameter. Find the approximate circumference and area of the smallest circle. First find the radius. The diameter is 2 centimeters, so the radius is } ( 2 ) 5 6 centimeters. 2 Then find the circumference and area. Use 3.4 for π. P 5 2πr ø 2( 3.4 )( 6 ) cm 5 πr 2 ø 3.4 ( 6 ) cm 2 Checkpoint Find the approximate circumference and area of the circle m C ø m; ø m 2 Example 3 Using a coordinate plane Triangle JKL has vertices J(, 6), K(6, 6), and L(3, 2). Find the approximate perimeter of triangle JKL. Write down your calculations to make sure you do not make a mistake substituting values in the Distance Formula. First draw triangle JKL in a coordinate plane. Then find the side lengths. ecause } JK is horizontal, use the Ruler Postulate to find JK. Use the Distance Formula to find JL and LK. JK units y J(,6) K(6, 6) L(3, 2) JL 5 Ï }}} ( 3 2 ) 2 (2 2 6 ) 2 5 Ï } 20 ø 4.5 units LK 5 Ï }}} ( 6 2 3) 2 ( 6 2 2) 2 5 Ï } units Then find the perimeter. P 5 JK JL LK ø units. x Copyright Holt McDougal. ll rights reserved. Lesson.7 Geometry Notetaking Guide 25

5 Your Notes Example 4 Solve a multi-step problem Lawn care You are using a roller to smooth a lawn. You can roll about 25 square yards in one minute. bout how many minutes does it take to roll a lawn that is 20 feet long and 75 feet wide? You can roll the lawn at a rate of 25 square yards per minute. So, the amount of time it takes you to roll the lawn depends on its. Step Find the area of the rectangular lawn. rea 5 lw 5 ( ) 5 ft 2 The rolling rate is in square yards per minute. Rewrite the area of the lawn in square yards. There are feet in yard, and 2 5 square feet in one square yard ft 2 p yd2 5 ft 2 yd2 Use unit analysis. Step 2 Write a verbal model to represent the situation. Then write and solve an equation based on the verbal model. Let t represent the total time (in minutes) needed to roll the lawn. rea of lawn (yd 2 ) 5 Rolling rate (yd 2 per min) 3 Total time (min) You can roll about 250 yards in 0 minutes. Use this fact to check that your solution is reasonable for the lawn area you found in Step. It takes about 5 p t Substitute. 5 t Divide each side by. minutes to roll the lawn. 26 Lesson.7 Geometry Notetaking Guide Copyright Holt McDougal. ll rights reserved.

6 Your Notes Example 4 Solve a multi-step problem Lawn care You are using a roller to smooth a lawn. You can roll about 25 square yards in one minute. bout how many minutes does it take to roll a lawn that is 20 feet long and 75 feet wide? You can roll the lawn at a rate of 25 square yards per minute. So, the amount of time it takes you to roll the lawn depends on its area. Step Find the area of the rectangular lawn. rea 5 lw 5 20 ( 75 ) ft 2 The rolling rate is in square yards per minute. Rewrite the area of the lawn in square yards. There are 3 feet in yard, and square feet in one square yard ft 2 p yd ft 2 yd2 Use unit analysis. Step 2 Write a verbal model to represent the situation. Then write and solve an equation based on the verbal model. Let t represent the total time (in minutes) needed to roll the lawn. rea of lawn (yd 2 ) 5 Rolling rate (yd 2 per min) 3 Total time (min) You can roll about 250 yards in 0 minutes. Use this fact to check that your solution is reasonable for the lawn area you found in Step p t Substitute. 8 5 t Divide each side by 25. It takes about 8 minutes to roll the lawn. 26 Lesson.7 Geometry Notetaking Guide Copyright Holt McDougal. ll rights reserved.

7 Your Notes In Example 5, you may want to make and label a sketch of the triangle. The sketch will not be exact, but it will help you visualize the given information. Example 5 The base of a triangle is 24 feet. Its area is 26 square feet. Find the height of the triangle. 5 Find unknown length rea of a triangle 5 Substitute. 5 Multiply. h 24 ft 5 h Solve for h. The height is feet. Checkpoint Complete the following exercises. 3. Find the perimeter of the triangle shown at the right. y (7, 6) (, ) C(7, 3) x 4. Suppose a lawn is half as long and half as wide as the lawn in Example 4. Will it take half the time to roll the lawn? Explain. Homework 5. The area of a triangle is 96 square inches, and its height is 8 inches. Find the length of its base. Copyright Holt McDougal. ll rights reserved. Lesson.7 Geometry Notetaking Guide 27

8 Your Notes In Example 5, you may want to make and label a sketch of the triangle. The sketch will not be exact, but it will help you visualize the given information. Example 5 The base of a triangle is 24 feet. Its area is 26 square feet. Find the height of the triangle. Find unknown length 5 } bh rea of a triangle } (24)(h) Substitute h Multiply. h 24 ft 8 5 h Solve for h. The height is 8 feet. Checkpoint Complete the following exercises. 3. Find the perimeter of the triangle shown at the right. about 7. units y (7, 6) (, ) C(7, 3) x 4. Suppose a lawn is half as long and half as wide as the lawn in Example 4. Will it take half the time to roll the lawn? Explain. No, it will take a quarter of the time to roll the lawn because it is a quarter of the original area. Homework 5. The area of a triangle is 96 square inches, and its height is 8 inches. Find the length of its base. 24 inches Copyright Holt McDougal. ll rights reserved. Lesson.7 Geometry Notetaking Guide 27

9 Words to Review Give an example of the vocabulary word. Point, line, plane Collinear points Coplanar points Line segment, endpoints Ray Opposite rays Intersection Postulate, axiom Coordinate Distance 28 Words to Review Geometry Notetaking Guide Copyright Holt McDougal. ll rights reserved.

10 Words to Review Give an example of the vocabulary word. Point, line, plane Collinear points line plane point Coplanar points D D and T are coplanar points. Ray X Y ###$ XY is a ray with initial point X. Intersection P T The intersection of two different lines is a point. and are collinear points. Line segment, endpoints C D } CD is a line segment with endpoints C and D. Opposite rays C If C is between and, then ###$ C and ###$ C are opposite rays. Postulate, axiom postulate, or axiom, is a rule that is accepted without proof. Coordinate Distance x x 2 The coordinates of points and are x and x 2. x x 2 5 x 2 2 x The distance between points and is x 2 2 x. 28 Words to Review Geometry Notetaking Guide Copyright Holt McDougal. ll rights reserved.

11 etween Congruent segments Midpoint Segment bisector ngle, sides, vertex Measure of an angle cute angle Right angle Obtuse angle Straight angle Copyright Holt McDougal. ll rights reserved. Words to Review Geometry Notetaking Guide 29

12 etween C Point C is between Points and. Midpoint Congruent segments C D } and } CD are congruent. Segment bisector M G M is the midpoint of }. ngle, sides, vertex FG is a segment bisector of }. Measure of an angle C Sides ###$ and ###$ C form. The vertex is. cute angle 408 The measure of is 408. Right angle 08 < m < 908 Obtuse angle m Straight angle 908 < m < 808 m Copyright Holt McDougal. ll rights reserved. Words to Review Geometry Notetaking Guide 29

13 ngle bisector, congruent angles Supplementary angles, linear pair Complementary angles, adjacent angles Vertical angles Polygon, side, vertex Concave, convex n-gon Equilateral, equiangular, regular Review your notes and Chapter by using the Chapter Review on pages 6 64 of your textbook. 30 Words to Review Geometry Notetaking Guide Copyright Holt McDougal. ll rights reserved.

14 ngle bisector, congruent angles C D Supplementary angles, linear pair X ###$ D is an angle bisector of CE. CD and DE are congruent. Complementary angles, adjacent angles E S STX and XTY are supplementary. STX and XTY are a linear pair. Vertical angles T Y R 2 P S QPR and RPS are complementary. QPR and RPS are adjacent. and 2 are vertical angles. Polygon, side, vertex Concave, convex polygon side vertex CD is concave. FGHJ is convex. F J D H C G n-gon n n-gon is a polygon with n sides. Equilateral, equiangular, regular The polygon is equilateral and equiangular, so it is regular. Review your notes and Chapter by using the Chapter Review on pages 6 64 of your textbook. 30 Words to Review Geometry Notetaking Guide Copyright Holt McDougal. ll rights reserved.

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

Geometry Chapter 1. 1.1 Point (pt) 1.1 Coplanar (1.1) 1.1 Space (1.1) 1.2 Line Segment (seg) 1.2 Measure of a Segment

Geometry Chapter 1. 1.1 Point (pt) 1.1 Coplanar (1.1) 1.1 Space (1.1) 1.2 Line Segment (seg) 1.2 Measure of a Segment Geometry Chapter 1 Section Term 1.1 Point (pt) Definition A location. It is drawn as a dot, and named with a capital letter. It has no shape or size. undefined term 1.1 Line A line is made up of points

More information

Five-Minute Check (over Lesson 1 5) CCSS Then/Now New Vocabulary Key Concepts: Polygons Example 1: Name and Classify Polygons Key Concepts:

Five-Minute Check (over Lesson 1 5) CCSS Then/Now New Vocabulary Key Concepts: Polygons Example 1: Name and Classify Polygons Key Concepts: Five-Minute Check (over Lesson 1 5) CCSS Then/Now New Vocabulary Key Concepts: Polygons Example 1: Name and Classify Polygons Key Concepts: Perimeter, Circumference, and Area Example 2: Find Perimeter

More information

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

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

More information

Study Guide and Review

Study Guide and Review Fill in the blank in each sentence with the vocabulary term that best completes the sentence. 1. A is a flat surface made up of points that extends infinitely in all directions. A plane is a flat surface

More 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

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

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

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

More information

Geometry: 1-1 Day 1 Points, Lines and Planes

Geometry: 1-1 Day 1 Points, Lines and Planes Geometry: 1-1 Day 1 Points, Lines and Planes What are the Undefined Terms? The Undefined Terms are: What is a Point? How is a point named? Example: What is a Line? A line is named two ways. What are the

More information

Geometry Unit 1. Basics of Geometry

Geometry Unit 1. Basics of Geometry Geometry Unit 1 Basics of Geometry Using inductive reasoning - Looking for patterns and making conjectures is part of a process called inductive reasoning Conjecture- an unproven statement that is based

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

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

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

Chapter 1: Essentials of Geometry

Chapter 1: Essentials of Geometry Section Section Title 1.1 Identify Points, Lines, and Planes 1.2 Use Segments and Congruence 1.3 Use Midpoint and Distance Formulas Chapter 1: Essentials of Geometry Learning Targets I Can 1. Identify,

More information

Name: Class: Date: Geometry Chapter 3 Review

Name: Class: Date: Geometry Chapter 3 Review Name: Class: Date: ID: A Geometry Chapter 3 Review. 1. The area of a rectangular field is 6800 square meters. If the width of the field is 80 meters, what is the perimeter of the field? Draw a diagram

More information

Geometry and Measurement

Geometry and Measurement The student will be able to: Geometry and Measurement 1. Demonstrate an understanding of the principles of geometry and measurement and operations using measurements Use the US system of measurement for

More information

1. A person has 78 feet of fencing to make a rectangular garden. What dimensions will use all the fencing with the greatest area?

1. A person has 78 feet of fencing to make a rectangular garden. What dimensions will use all the fencing with the greatest area? 1. A person has 78 feet of fencing to make a rectangular garden. What dimensions will use all the fencing with the greatest area? (a) 20 ft x 19 ft (b) 21 ft x 18 ft (c) 22 ft x 17 ft 2. Which conditional

More information

GEOMETRY FINAL EXAM REVIEW

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

More information

Characteristics of the Four Main Geometrical Figures

Characteristics of the Four Main Geometrical Figures Math 40 9.7 & 9.8: The Big Four Square, Rectangle, Triangle, Circle Pre Algebra We will be focusing our attention on the formulas for the area and perimeter of a square, rectangle, triangle, and a circle.

More information

Final Review Geometry A Fall Semester

Final Review Geometry A Fall Semester Final Review Geometry Fall Semester Multiple Response Identify one or more choices that best complete the statement or answer the question. 1. Which graph shows a triangle and its reflection image over

More information

2. Sketch and label two different isosceles triangles with perimeter 4a + b. 3. Sketch an isosceles acute triangle with base AC and vertex angle B.

2. Sketch and label two different isosceles triangles with perimeter 4a + b. 3. Sketch an isosceles acute triangle with base AC and vertex angle B. Section 1.5 Triangles Notes Goal of the lesson: Explore the properties of triangles using Geometer s Sketchpad Define and classify triangles and their related parts Practice writing more definitions Learn

More information

acute angle adjacent angles angle bisector between axiom Vocabulary Flash Cards Chapter 1 (p. 39) Chapter 1 (p. 48) Chapter 1 (p.38) Chapter 1 (p.

acute angle adjacent angles angle bisector between axiom Vocabulary Flash Cards Chapter 1 (p. 39) Chapter 1 (p. 48) Chapter 1 (p.38) Chapter 1 (p. Vocabulary Flash ards acute angle adjacent angles hapter 1 (p. 39) hapter 1 (p. 48) angle angle bisector hapter 1 (p.38) hapter 1 (p. 42) axiom between hapter 1 (p. 12) hapter 1 (p. 14) collinear points

More information

Area Long-Term Memory Review Review 1

Area Long-Term Memory Review Review 1 Review 1 1. To find the perimeter of any shape you all sides of the shape.. To find the area of a square, you the length and width. 4. What best identifies the following shape. Find the area and perimeter

More information

Geometry: Unit 1 Vocabulary TERM DEFINITION GEOMETRIC FIGURE. Cannot be defined by using other figures.

Geometry: Unit 1 Vocabulary TERM DEFINITION GEOMETRIC FIGURE. Cannot be defined by using other figures. Geometry: Unit 1 Vocabulary 1.1 Undefined terms Cannot be defined by using other figures. Point A specific location. It has no dimension and is represented by a dot. Line Plane A connected straight path.

More information

Topics Covered on Geometry Placement Exam

Topics Covered on Geometry Placement Exam Topics Covered on Geometry Placement Exam - Use segments and congruence - Use midpoint and distance formulas - Measure and classify angles - Describe angle pair relationships - Use parallel lines and transversals

More information

8-3 Perimeter and Circumference

8-3 Perimeter and Circumference Learn to find the perimeter of a polygon and the circumference of a circle. 8-3 Perimeter Insert Lesson and Title Circumference Here perimeter circumference Vocabulary The distance around a geometric figure

More information

2 feet Opposite sides of a rectangle are equal. All sides of a square are equal. 2 X 3 = 6 meters = 18 meters

2 feet Opposite sides of a rectangle are equal. All sides of a square are equal. 2 X 3 = 6 meters = 18 meters GEOMETRY Vocabulary 1. Adjacent: Next to each other. Side by side. 2. Angle: A figure formed by two straight line sides that have a common end point. A. Acute angle: Angle that is less than 90 degree.

More information

INDEX. Arc Addition Postulate,

INDEX. Arc Addition Postulate, # 30-60 right triangle, 441-442, 684 A Absolute value, 59 Acute angle, 77, 669 Acute triangle, 178 Addition Property of Equality, 86 Addition Property of Inequality, 258 Adjacent angle, 109, 669 Adjacent

More 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

Practice Test - Chapter 1. Use the figure to name each of the following.

Practice Test - Chapter 1. Use the figure to name each of the following. Use the figure to name each of the following. 1. the line that contains points Q and Z The points Q and Z lie on the line b, line b 2. two points that are coplanar with points W, X, and Y Coplanar points

More information

BASIC GEOMETRY GLOSSARY

BASIC GEOMETRY GLOSSARY BASIC GEOMETRY GLOSSARY Acute angle An angle that measures between 0 and 90. Examples: Acute triangle A triangle in which each angle is an acute angle. Adjacent angles Two angles next to each other that

More information

Tallahassee Community College PERIMETER

Tallahassee Community College PERIMETER Tallahassee Community College 47 PERIMETER The perimeter of a plane figure is the distance around it. Perimeter is measured in linear units because we are finding the total of the lengths of the sides

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

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

Algebra Geometry Glossary. 90 angle

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

More information

1. A student followed the given steps below to complete a construction. Which type of construction is best represented by the steps given above?

1. A student followed the given steps below to complete a construction. Which type of construction is best represented by the steps given above? 1. A student followed the given steps below to complete a construction. Step 1: Place the compass on one endpoint of the line segment. Step 2: Extend the compass from the chosen endpoint so that the width

More information

Geometry Notes PERIMETER AND AREA

Geometry Notes PERIMETER AND AREA Perimeter and Area Page 1 of 57 PERIMETER AND AREA Objectives: After completing this section, you should be able to do the following: Calculate the area of given geometric figures. Calculate the perimeter

More information

4-1 Classifying Triangles. ARCHITECTURE Classify each triangle as acute, equiangular, obtuse, or right. 1. Refer to the figure on page 240.

4-1 Classifying Triangles. ARCHITECTURE Classify each triangle as acute, equiangular, obtuse, or right. 1. Refer to the figure on page 240. ARCHITECTURE Classify each triangle as acute, equiangular, obtuse, or right. 1. Refer to the figure on page 240. Classify each triangle as acute, equiangular, obtuse, or right. Explain your reasoning.

More information

2006 Geometry Form A Page 1

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

More information

Areas of Rectangles and Parallelograms

Areas of Rectangles and Parallelograms CONDENSED LESSON 8.1 Areas of Rectangles and Parallelograms In this lesson you will Review the formula for the area of a rectangle Use the area formula for rectangles to find areas of other shapes Discover

More information

1-6 Two-Dimensional Figures. Name each polygon by its number of sides. Then classify it as convex or concave and regular or irregular.

1-6 Two-Dimensional Figures. Name each polygon by its number of sides. Then classify it as convex or concave and regular or irregular. Stop signs are constructed in the shape of a polygon with 8 sides of equal length The polygon has 8 sides A polygon with 8 sides is an octagon All sides of the polygon are congruent and all angles are

More information

Perimeter. 14ft. 5ft. 11ft.

Perimeter. 14ft. 5ft. 11ft. Perimeter The perimeter of a geometric figure is the distance around the figure. The perimeter could be thought of as walking around the figure while keeping track of the distance traveled. To determine

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

GEOMETRY. Chapter 1: Foundations for Geometry. Name: Teacher: Pd:

GEOMETRY. Chapter 1: Foundations for Geometry. Name: Teacher: Pd: GEOMETRY Chapter 1: Foundations for Geometry Name: Teacher: Pd: Table of Contents Lesson 1.1: SWBAT: Identify, name, and draw points, lines, segments, rays, and planes. Pgs: 1-4 Lesson 1.2: SWBAT: Use

More information

Student Outcomes. Lesson Notes. Classwork. Exercises 1 3 (4 minutes)

Student Outcomes. Lesson Notes. Classwork. Exercises 1 3 (4 minutes) Student Outcomes Students give an informal derivation of the relationship between the circumference and area of a circle. Students know the formula for the area of a circle and use it to solve problems.

More information

Euclidean Geometry. We start with the idea of an axiomatic system. An axiomatic system has four parts:

Euclidean Geometry. We start with the idea of an axiomatic system. An axiomatic system has four parts: Euclidean Geometry Students are often so challenged by the details of Euclidean geometry that they miss the rich structure of the subject. We give an overview of a piece of this structure below. We start

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

55 questions (multiple choice, check all that apply, and fill in the blank) The exam is worth 220 points.

55 questions (multiple choice, check all that apply, and fill in the blank) The exam is worth 220 points. Geometry Core Semester 1 Semester Exam Preparation Look back at the unit quizzes and diagnostics. Use the unit quizzes and diagnostics to determine which topics you need to review most carefully. The unit

More information

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

(a) 5 square units. (b) 12 square units. (c) 5 3 square units. 3 square units. (d) 6. (e) 16 square units 1. Find the area of parallelogram ACD shown below if the measures of segments A, C, and DE are 6 units, 2 units, and 1 unit respectively and AED is a right angle. (a) 5 square units (b) 12 square units

More information

Geometry Chapter 1 Vocabulary. coordinate - The real number that corresponds to a point on a line.

Geometry Chapter 1 Vocabulary. coordinate - The real number that corresponds to a point on a line. Chapter 1 Vocabulary coordinate - The real number that corresponds to a point on a line. point - Has no dimension. It is usually represented by a small dot. bisect - To divide into two congruent parts.

More information

1.2 Informal Geometry

1.2 Informal Geometry 1.2 Informal Geometry Mathematical System: (xiomatic System) Undefined terms, concepts: Point, line, plane, space Straightness of a line, flatness of a plane point lies in the interior or the exterior

More information

Chapter 3.1 Angles. Geometry. Objectives: Define what an angle is. Define the parts of an angle.

Chapter 3.1 Angles. Geometry. Objectives: Define what an angle is. Define the parts of an angle. Chapter 3.1 Angles Define what an angle is. Define the parts of an angle. Recall our definition for a ray. A ray is a line segment with a definite starting point and extends into infinity in only one direction.

More information

Perimeter and area formulas for common geometric figures:

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

More information

Area. Area Overview. Define: Area:

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

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

Archdiocese of Washington Catholic Schools Academic Standards Mathematics

Archdiocese of Washington Catholic Schools Academic Standards Mathematics 5 th GRADE Archdiocese of Washington Catholic Schools Standard 1 - Number Sense Students compute with whole numbers*, decimals, and fractions and understand the relationship among decimals, fractions,

More information

Chapter 1. Foundations of Geometry: Points, Lines, and Planes

Chapter 1. Foundations of Geometry: Points, Lines, and Planes Chapter 1 Foundations of Geometry: Points, Lines, and Planes Objectives(Goals) Identify and model points, lines, and planes. Identify collinear and coplanar points and intersecting lines and planes in

More information

Surface Area of Rectangular & Right Prisms Surface Area of Pyramids. Geometry

Surface Area of Rectangular & Right Prisms Surface Area of Pyramids. Geometry Surface Area of Rectangular & Right Prisms Surface Area of Pyramids Geometry Finding the surface area of a prism A prism is a rectangular solid with two congruent faces, called bases, that lie in parallel

More information

CCGPS UNIT 3 Semester 1 ANALYTIC GEOMETRY Page 1 of 32. Circles and Volumes Name:

CCGPS UNIT 3 Semester 1 ANALYTIC GEOMETRY Page 1 of 32. Circles and Volumes Name: GPS UNIT 3 Semester 1 NLYTI GEOMETRY Page 1 of 3 ircles and Volumes Name: ate: Understand and apply theorems about circles M9-1.G..1 Prove that all circles are similar. M9-1.G.. Identify and describe relationships

More information

GEOMETRY CONCEPT MAP. Suggested Sequence:

GEOMETRY CONCEPT MAP. Suggested Sequence: CONCEPT MAP GEOMETRY August 2011 Suggested Sequence: 1. Tools of Geometry 2. Reasoning and Proof 3. Parallel and Perpendicular Lines 4. Congruent Triangles 5. Relationships Within Triangles 6. Polygons

More information

Classify each triangle as acute, equiangular, obtuse, or right. Explain your reasoning.

Classify each triangle as acute, equiangular, obtuse, or right. Explain your reasoning. ARCHITECTURE Classify each triangle as acute, equiangular, obtuse, or right. 1. Refer to the figure on page 240. One angle of the triangle measures 90, so it is a right angle. Since the triangle has a

More information

Geometry Final Assessment 11-12, 1st semester

Geometry Final Assessment 11-12, 1st semester Geometry Final ssessment 11-12, 1st semester Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Name three collinear points. a. P, G, and N c. R, P, and G

More information

SURFACE AREA AND VOLUME

SURFACE AREA AND VOLUME SURFACE AREA AND VOLUME In this unit, we will learn to find the surface area and volume of the following threedimensional solids:. Prisms. Pyramids 3. Cylinders 4. Cones It is assumed that the reader has

More information

10.1: Areas of Parallelograms and Triangles

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

More information

Lesson 12.1 Skills Practice

Lesson 12.1 Skills Practice Lesson 12.1 Skills Practice Name Date Introduction to Circles Circle, Radius, and Diameter Vocabulary Define each term in your own words. 1. circle A circle is a collection of points on the same plane

More information

Area of Parallelograms (pages 546 549)

Area of Parallelograms (pages 546 549) A Area of Parallelograms (pages 546 549) A parallelogram is a quadrilateral with two pairs of parallel sides. The base is any one of the sides and the height is the shortest distance (the length of a perpendicular

More information

100 Math Facts 6 th Grade

100 Math Facts 6 th Grade 100 Math Facts 6 th Grade Name 1. SUM: What is the answer to an addition problem called? (N. 2.1) 2. DIFFERENCE: What is the answer to a subtraction problem called? (N. 2.1) 3. PRODUCT: What is the answer

More information

Honors Geometry Final Exam Study Guide

Honors Geometry Final Exam Study Guide 2011-2012 Honors Geometry Final Exam Study Guide Multiple Choice Identify the choice that best completes the statement or answers the question. 1. In each pair of triangles, parts are congruent as marked.

More information

1.1 Identify Points, Lines, and Planes

1.1 Identify Points, Lines, and Planes 1.1 Identify Points, Lines, and Planes Objective: Name and sketch geometric figures. Key Vocabulary Undefined terms - These words do not have formal definitions, but there is agreement aboutwhat they mean.

More information

Cumulative Test. 161 Holt Geometry. Name Date Class

Cumulative Test. 161 Holt Geometry. Name Date Class Choose the best answer. 1. P, W, and K are collinear, and W is between P and K. PW 10x, WK 2x 7, and PW WK 6x 11. What is PK? A 2 C 90 B 6 D 11 2. RM bisects VRQ. If mmrq 2, what is mvrm? F 41 H 9 G 2

More information

Definitions, Postulates and Theorems

Definitions, Postulates and Theorems Definitions, s and s Name: Definitions Complementary Angles Two angles whose measures have a sum of 90 o Supplementary Angles Two angles whose measures have a sum of 180 o A statement that can be proven

More information

Perimeter, Circumference, and Area

Perimeter, Circumference, and Area -9 Perimeter, Circumference, and Area -9. Plan What You ll Learn To find perimeters of rectangles and squares, and circumferences of circles To find areas of rectangles, squares, and circles... And Why

More information

Section 7.2 Area. The Area of Rectangles and Triangles

Section 7.2 Area. The Area of Rectangles and Triangles Section 7. Area The Area of Rectangles and Triangles We encounter two dimensional objects all the time. We see objects that take on the shapes similar to squares, rectangle, trapezoids, triangles, and

More information

Perimeter is the length of the boundary of a two dimensional figure.

Perimeter is the length of the boundary of a two dimensional figure. Section 2.2: Perimeter and Area Perimeter is the length of the boundary of a two dimensional figure. The perimeter of a circle is called the circumference. The perimeter of any two dimensional figure whose

More information

CSU Fresno Problem Solving Session. Geometry, 17 March 2012

CSU Fresno Problem Solving Session. Geometry, 17 March 2012 CSU Fresno Problem Solving Session Problem Solving Sessions website: http://zimmer.csufresno.edu/ mnogin/mfd-prep.html Math Field Day date: Saturday, April 21, 2012 Math Field Day website: http://www.csufresno.edu/math/news

More information

of one triangle are congruent to the corresponding parts of the other triangle, the two triangles are congruent.

of one triangle are congruent to the corresponding parts of the other triangle, the two triangles are congruent. 2901 Clint Moore Road #319, Boca Raton, FL 33496 Office: (561) 459-2058 Mobile: (949) 510-8153 Email: HappyFunMathTutor@gmail.com www.happyfunmathtutor.com GEOMETRY THEORUMS AND POSTULATES GEOMETRY POSTULATES:

More information

LEVEL G, SKILL 1. Answers Be sure to show all work.. Leave answers in terms of ϖ where applicable.

LEVEL G, SKILL 1. Answers Be sure to show all work.. Leave answers in terms of ϖ where applicable. Name LEVEL G, SKILL 1 Class Be sure to show all work.. Leave answers in terms of ϖ where applicable. 1. What is the area of a triangle with a base of 4 cm and a height of 6 cm? 2. What is the sum of the

More information

Student Name: Teacher: Date: District: Miami-Dade County Public Schools. Assessment: 9_12 Mathematics Geometry Exam 1

Student Name: Teacher: Date: District: Miami-Dade County Public Schools. Assessment: 9_12 Mathematics Geometry Exam 1 Student Name: Teacher: Date: District: Miami-Dade County Public Schools Assessment: 9_12 Mathematics Geometry Exam 1 Description: GEO Topic 1 Test: Tools of Geometry Form: 201 1. A student followed the

More information

Postulate 17 The area of a square is the square of the length of a. Postulate 18 If two figures are congruent, then they have the same.

Postulate 17 The area of a square is the square of the length of a. Postulate 18 If two figures are congruent, then they have the same. Chapter 11: Areas of Plane Figures (page 422) 11-1: Areas of Rectangles (page 423) Rectangle Rectangular Region Area is measured in units. Postulate 17 The area of a square is the square of the length

More information

Calculating Area, Perimeter and Volume

Calculating Area, Perimeter and Volume Calculating Area, Perimeter and Volume You will be given a formula table to complete your math assessment; however, we strongly recommend that you memorize the following formulae which will be used regularly

More information

SA B 1 p where is the slant height of the pyramid. V 1 3 Bh. 3D Solids Pyramids and Cones. Surface Area and Volume of a Pyramid

SA B 1 p where is the slant height of the pyramid. V 1 3 Bh. 3D Solids Pyramids and Cones. Surface Area and Volume of a Pyramid Accelerated AAG 3D Solids Pyramids and Cones Name & Date Surface Area and Volume of a Pyramid The surface area of a regular pyramid is given by the formula SA B 1 p where is the slant height of the pyramid.

More information

Geometry Unit 7 (Textbook Chapter 9) Solving a right triangle: Find all missing sides and all missing angles

Geometry Unit 7 (Textbook Chapter 9) Solving a right triangle: Find all missing sides and all missing angles Geometry Unit 7 (Textbook Chapter 9) Name Objective 1: Right Triangles and Pythagorean Theorem In many geometry problems, it is necessary to find a missing side or a missing angle of a right triangle.

More information

1.1. Building Blocks of Geometry EXAMPLE. Solution a. P is the midpoint of both AB and CD. Q is the midpoint of GH. CONDENSED

1.1. Building Blocks of Geometry EXAMPLE. Solution a. P is the midpoint of both AB and CD. Q is the midpoint of GH. CONDENSED CONDENSED LESSON 1.1 Building Blocks of Geometry In this lesson you will Learn about points, lines, and planes and how to represent them Learn definitions of collinear, coplanar, line segment, congruent

More information

GEOMETRY CIRCLING THE BASES

GEOMETRY CIRCLING THE BASES LESSON 3: PRE-VISIT - PERIMETER AND AREA OBJECTIVE: Students will be able to: Distinguish between area and perimeter. Calculate the perimeter of a polygon whose side lengths are given or can be determined.

More information

Picture. Right Triangle. Acute Triangle. Obtuse Triangle

Picture. Right Triangle. Acute Triangle. Obtuse Triangle Name Perpendicular Bisector of each side of a triangle. Construct the perpendicular bisector of each side of each triangle. Point of Concurrency Circumcenter Picture The circumcenter is equidistant from

More information

Picture. Right Triangle. Acute Triangle. Obtuse Triangle

Picture. Right Triangle. Acute Triangle. Obtuse Triangle Name Perpendicular Bisector of each side of a triangle. Construct the perpendicular bisector of each side of each triangle. Point of Concurrency Circumcenter Picture The circumcenter is equidistant from

More information

#2. Isosceles Triangle Theorem says that If a triangle is isosceles, then its BASE ANGLES are congruent.

#2. Isosceles Triangle Theorem says that If a triangle is isosceles, then its BASE ANGLES are congruent. 1 Geometry Proofs Reference Sheet Here are some of the properties that we might use in our proofs today: #1. Definition of Isosceles Triangle says that If a triangle is isosceles then TWO or more sides

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

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2015 8:30 to 11:30 a.m., only.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2015 8:30 to 11:30 a.m., only. GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 13, 2015 8:30 to 11:30 a.m., only Student Name: School Name: The possession or use of any communications

More information

Geometry Regents Review

Geometry Regents Review Name: Class: Date: Geometry Regents Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. If MNP VWX and PM is the shortest side of MNP, what is the shortest

More information

Chapter One. Points, Lines, Planes, and Angles

Chapter One. Points, Lines, Planes, and Angles Chapter One Points, Lines, Planes, and Angles Objectives A. Use the terms defined in the chapter correctly. B. Properly use and interpret the symbols for the terms and concepts in this chapter. C. Appropriately

More information

GEOMETRY. Constructions OBJECTIVE #: G.CO.12

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

More information

How do changes in dimensions of similar geometric figures affect the perimeters and the areas of the figures? ACTIVITY: Creating Similar Figures

How do changes in dimensions of similar geometric figures affect the perimeters and the areas of the figures? ACTIVITY: Creating Similar Figures .6 Perimeters and Areas of Similar Figures How do changes in dimensions of similar geometric figures affect the perimeters and the areas of the figures? ACTIVITY: Creating Similar Figures Work with a partner.

More information

Working in 2 & 3 dimensions Revision Guide

Working in 2 & 3 dimensions Revision Guide Tips for Revising Working in 2 & 3 dimensions Make sure you know what you will be tested on. The main topics are listed below. The examples show you what to do. List the topics and plan a revision timetable.

More information

10-4 Inscribed Angles. Find each measure. 1.

10-4 Inscribed Angles. Find each measure. 1. Find each measure. 1. 3. 2. intercepted arc. 30 Here, is a semi-circle. So, intercepted arc. So, 66 4. SCIENCE The diagram shows how light bends in a raindrop to make the colors of the rainbow. If, what

More information

Tangent Properties. Line m is a tangent to circle O. Point T is the point of tangency.

Tangent Properties. Line m is a tangent to circle O. Point T is the point of tangency. CONDENSED LESSON 6.1 Tangent Properties In this lesson you will Review terms associated with circles Discover how a tangent to a circle and the radius to the point of tangency are related Make a conjecture

More information

Conjectures for Geometry for Math 70 By I. L. Tse

Conjectures for Geometry for Math 70 By I. L. Tse Conjectures for Geometry for Math 70 By I. L. Tse Chapter Conjectures 1. Linear Pair Conjecture: If two angles form a linear pair, then the measure of the angles add up to 180. Vertical Angle Conjecture:

More information

CHAPTER 8, GEOMETRY. 4. A circular cylinder has a circumference of 33 in. Use 22 as the approximate value of π and find the radius of this cylinder.

CHAPTER 8, GEOMETRY. 4. A circular cylinder has a circumference of 33 in. Use 22 as the approximate value of π and find the radius of this cylinder. TEST A CHAPTER 8, GEOMETRY 1. A rectangular plot of ground is to be enclosed with 180 yd of fencing. If the plot is twice as long as it is wide, what are its dimensions? 2. A 4 cm by 6 cm rectangle has

More information

Jumpstarters for Geometry

Jumpstarters for Geometry Jumpstarters for Geometry Short Daily Warm-ups for the Classroom y Vicky ShiotSU COPYRIGHT 2007 Mark Twain Media, Inc. ISN 978-1-58037-399-9 Printing No. CD-404058 Mark Twain Media, Inc., Publishers Distributed

More information

Grade 3 Math Expressions Vocabulary Words

Grade 3 Math Expressions Vocabulary Words Grade 3 Math Expressions Vocabulary Words Unit 1, Book 1 Place Value and Multi-Digit Addition and Subtraction OSPI words not used in this unit: add, addition, number, more than, subtract, subtraction,

More information