# Pre-Algebra Interactive Chalkboard Copyright by The McGraw-Hill Companies, Inc. Send all inquiries to:

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Pre-Algebra Interactive Chalkboard Copyright by The McGraw-Hill Companies, Inc. Send all inquiries to: GLENCOE DIVISION Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240

2

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

4 Lesson 9-1 Squares and Square Roots Lesson 9-2 The Real Number System Lesson 9-3 Angles Lesson 9-4 Triangles Lesson 9-5 The Pythagorean Theorem Lesson 9-6 The Distance and Midpoint Formulas Lesson 9-7 Similar Triangles and Indirect Measurement Lesson 9-8 Sine, Cosine, and Tangent Ratios

5 Example 1 Find Square Roots Example 2 Calculate Square Roots Example 3 Estimate Square Roots Example 4 Use Square Roots to Solve a Problem

6 Find. indicates the positive square root of 64. Since Answer: 8

7 Find. indicates the negative square root of 121. Since Answer: 11

8 Find. indicates both square roots of 4. Since Answer: 2 and 2

10 Use a calculator to find nearest tenth. to the 2nd [ ] 23 ENTER Use a calculator. Round to the nearest tenth. Answer: 4.8 Check Since, the answer is reasonable.

11 Use a calculator to find nearest tenth. to the 2nd [ ] 46 ENTER Use a calculator. Round to the nearest tenth. Answer: 6.8 Check Since, the answer is reasonable.

12 Use a calculator to find each square root to the nearest tenth. a. Answer: 8.4 b. Answer: 6.2

13 Estimate to the nearest whole number. Find the two perfect squares closest to 22. To do this, list some perfect squares. 1, 4, 9, 16, 25, 16 and 25 are closest to 22.

14 16 < 22 < is between 16 and 25. < < 4 < < 5 is between and. and. Since 22 is closer to 25 than 16, the best whole number estimate for is 5. Answer: 5

15 Estimate to the nearest whole number. Find the two perfect squares closest to 319. To do this, list some perfect squares...., 225, 256, 289, 324, 289 and 324 are closest to 319.

16 324 < 319 < is between 324 and 289. < < is between and. 18 < < 17 and.

17 Since 319 is closer to 324 than 289, the best whole number estimate for is 18. Check Answer: 18

18 Estimate each square root to the nearest whole number. a. Answer: 7 b. Answer: 12

19 Landmarks The observation deck at the Seattle Space Needle is 520 feet above the ground. On a clear day, about how far could a tourist on the deck see? Round to the nearest tenth. Use the formula where D is the distance in miles and A is the altitude, or height, in feet. Write the formula. Replace A with 520. Evaluate the square root first.

20 Multiply. Answer: On a clear day, a tourist could see about 27.8 miles.

21 Skyscraper A skyscraper stands 378 feet high. On a clear day, about how far could an individual standing on the roof of the skyscraper see? Round to the nearest tenth. Answer: On a clear day, an individual could see about 23.7 miles.

22

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

24 Example 1 Classify Real Numbers Example 2 Compare Real Numbers on a Number Line Example 3 Solve Equations

25 Name all of the sets of numbers to which the real number 17 belongs. Answer: This number is a natural number, a whole number, an integer, and a rational number.

26 Name all of the sets of numbers to which the real number belongs. Answer: Since, this number is an integer and a rational number.

27 Name all of the sets of numbers to which the real number belongs. Answer: Since, this number is a natural number, a whole number, an integer, and a rational number.

28 Name all of the sets of numbers to which the real number belongs. Answer: This repeating decimal is a rational number because it is equivalent to.

29 Name all of the sets of numbers to which the real number belongs. Answer: It is not the square root of a perfect square so it is irrational.

30 Name all of the sets of numbers to which each real number belongs. a. 31 b. Answer: natural number, whole number, integer, rational number Answer: integer, rational number c d. e. Answer: rational number Answer: natural number, whole number, integer, rational number Answer: irrational number

31 Replace with <, >, or = to make true statement. a Express each number as a decimal. Then graph the numbers.

32 Answer: Since is to the left of

33 Order from least to greatest. Express each number as a decimal. Then compare the decimals.

34 Answer: From least to greatest, the order is

35 a. Replace with <, >, or = to make a true statement. Answer: > b. Order from least to greatest. Answer:

36 Solve if necessary.. Round to the nearest tenth, Write the equation. Take the square root of each side. Find the positive and negative square root. Answer: The solutions are 13 and 13.

37 Solve if necessary.. Round to the nearest tenth, Write the equation. Answer: The solutions are 7.1 and 7.1. Take the square root of each side. Find the positive and negative square root. Use a calculator.

38 Solve each equation. Round to the nearest tenth, if necessary. a. b. Answer: 9 and 9 Answer: 4.9 and 4.9

39

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

41 Example 1 Measure Angles Example 2 Draw Angles Example 3 Classify Angles Example 4 Use Angles to Solve a Problem

42 Use a protractor to measure RSW. Step 1 Place the center point of the protractor s base on vertex S. Align the straight edge with side so that the marker for 0 is on the ray.

43 Use a protractor to measure RSW. 42 Step 2 Use the scale that begins with 0 at where the other side of the angle,, crosses this scale.. Read

44 Use a protractor to measure RSW. 42 Answer: The measure of angle RSW is 42. Using symbols,

45 Find the measurements of GUM, SUM, and BUG. 120 Answer: is at 0 on the right.

46 Find the measurements of GUM, SUM, and BUG. 32 Answer: is at 0 on the right.

47 Find the measurements of GUM, SUM, and BUG. 60 Answer: is at 0 on the left.

48 a. Use a protractor to measure ABC. Answer: 75

49 b. Find the measures of FDE, GDE, and HDG. Answer: FDE = 37, GDE = 118, HDG = 62

50 Draw R having a measurement of 145. R Step 1 Draw a ray with endpoint R.

51 Draw R having a measurement of 145. Step 2 Place the center point of the protractor on R. Align the mark labeled 0 with the ray. R

52 Draw R having a measurement of R Step 3 Use the scale that begins with 0. Locate the mark labeled 145. Then draw the other side of the angle.

54 Draw M having a measurement of 47. Answer:

55 Classify the angle as acute, obtuse, right, or straight. m KLM < 90. Answer: KLM is acute.

56 Classify the angle as acute, obtuse, right, or straight. m NPQ = 180. Answer: NPQ is straight.

57 Classify the angle as acute, obtuse, right, or straight. m RST > 90. Answer: RST is obtuse.

58 Classify each angle as acute, obtuse, right, or straight. a. Answer: right b. Answer: obtuse

59 Classify each angle as acute, obtuse, right, or straight. c. Answer: straight

60 The diagram shows the angle between the back of a chair and the seat of the chair. Classify this angle. Answer: Since 95 is greater than 90, the angle is obtuse.

61 The diagram shows the angle between the bed of the truck and the frame of the truck. Classify this angle. Answer: The angle is acute.

62

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

64 Example 1 Find Angle Measures Example 2 Use Ratios to Find Angle Measures Example 3 Classify Triangles

65 Find the value of x in DEF. The sum of the measures is 180. Replace m D with 100 and m E with 33. Simplify.

66 Answer: The measure of F is 47. Subtract 133 from each side.

67 Find the value of x in MNO. Answer: The measure of N is 57.

68 Algebra The measures of the angles of a certain triangle are in the ratio 2:3:5. What are the measures of the angles? Words Variables Equation The measures of the angles are in the ratio 2:3:5. Let 2x represent the measure of one angle, 3x the measure of a second angle, and 5x the measure of the third angle. The sum of the measures is 180.

69 Combine like terms. Divide each side by 10. Simplify. Since Answer: The measures of the angles are 36, 54, and 90.

70 Check So, the answer is correct.

71 Algebra The measures of the angles of a certain triangle are in the ratio 3:5:7. What are the measures of the angles? Answer: The measures of the angles are 36, 60, and 84.

72 Classify the triangle by its angles and by its sides. Angles Sides All angles are acute. All sides are congruent. Answer: The triangle is an acute equilateral triangle.

73 Classify the triangle by its angles and by its sides. Angles Sides The triangle has a right angle. The triangle has no congruent sides. Answer: The triangle is a right scalene triangle.

74 Classify each triangle by its angles and by its sides. a. Answer: obtuse scalene b. Answer: acute equilateral

75

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

77 Example 1 Find the Length of the Hypotenuse Example 2 Solve a Right Triangle Example 3 Use the Pythagorean Theorem Example 4 Identify a Right Triangle

78 Find the length of the hypotenuse of the right triangle. Pythagorean Theorem Replace a with 21 and b with 20. Evaluate 21 2 and Add 441 and 400.

79 Take the square root of each side. Answer: The length of the hypotenuse is 29 feet.

80 Find the length of the hypotenuse of the right triangle. Answer: The length of the hypotenuse is 5 meters.

81 Find the length of the leg of the right triangle. Pythagorean Theorem Replace c with 11 and a with 8. Evaluate 11 2 and 8 2.

82 Subtract 64 from each side. Simplify. Take the square root of each side. 2nd [ ] 57 ENTER Answer: The length of the leg is about 7.5 meters.

83 Find the length of the leg of the right triangle. Answer: The length of the leg is about 12.7 inches.

84 Multiple-Choice Test Item A building is 10 feet tall. A ladder is positioned against the building so that the base of the ladder is 3 feet from the building. How long is the ladder? A 12.4 feet C 10.0 feet B 10.4 feet D 14.9 feet Read the Test Item Make a drawing to illustrate the problem. The ladder, ground, and side of the house form a right triangle.

85 Solve the Test Item Use the Pythagorean Theorem to find the length of the ladder. Pythagorean Theorem Replace a with 3 and b with 10. Evaluate 3 2 and Simplify.

86 Take the square root of each side. Round to the nearest tenth. The ladder is about 10.4 feet tall. Answer: The answer is B.

87 Multiple-Choice Test Item An 18-foot ladder is placed against a building which is 14 feet tall. About how far is the base of the ladder from the building? A 11.6 feet C 11.3 feet B 10.9 feet D 11.1 feet Answer: The answer is C.

88 The measures of three sides of a triangle are given. Determine whether the triangle is a right triangle. 48 ft, 60 ft, 78 ft The triangle is not a right triangle. Answer: no Pythagorean Theorem Replace a with 48, b with 60, and c with 78. Evaluate. Simplify.

89 The measures of three sides of a triangle are given. Determine whether the triangle is a right triangle. 24 cm, 70 cm, 74 cm The triangle is a right triangle. Answer: yes Pythagorean Theorem Replace a with 24, b with 70, and c with 74. Evaluate. Simplify.

90 The measures of three sides of a triangle are given. Determine whether each triangle is a right triangle. a. 42 in., 61 in., 84 in. Answer: no b. 16 m, 30 m, 34 m Answer: yes

91

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

93 Example 1 Use the Distance Formula Example 2 Use the Distance Formula to Solve a Problem Example 3 Use the Midpoint Formula

94 Find the distance between M(8, 4) and N( 6, 2). Round to the nearest tenth, if necessary. Use the Distance Formula. Distance Formula Simplify.

95 Evaluate ( 14) 2 and ( 6) 2. Add 196 and 36. Take the square root. Answer: The distance between points M and N is about 15.2 units.

96 Find the distance between A( 4, 5) and B(3, 9). Round to the nearest tenth, if necessary. Answer: The distance between points A and B is about 15.7 units.

97 Geometry Find the perimeter of XYZ to the nearest tenth. First, use the Distance Formula to find the length of each side of the triangle.

98 Distance Formula Simplify. Evaluate powers. Simplify.

99 Distance Formula Simplify. Evaluate powers. Simplify.

100 Distance Formula Simplify. Evaluate powers. Simplify.

101 Then add the lengths of the sides to find the perimeter. Answer: The perimeter is about 15.8 units.

102 Geometry Find the perimeter of ABC to the nearest tenth. Answer: The perimeter is about 21.3 units.

103 Find the coordinates of the midpoint of

104 Midpoint Formula Substitution Simplify. Answer: The coordinates of the midpoint of are (3, 3).

105 Find the coordinates of the midpoint of Answer: The coordinates of the midpoint of are (1, 1).

106

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

108 Example 1 Find Measures of Similar Triangles Example 2 Use Indirect Measurement Example 3 Use Shadow Reckoning

109 If RUN ~ CAB, what is the value of x? The corresponding sides are proportional. Write a proportion.

110 Replace UR with 4, AC with 8, UN with 10, and AB with x. Find the cross products. Simplify. Mentally divide each side by 4. Answer: The value of x is 20.

111 If ABC ~ DEF, what is the value of x? Answer: The value of x is 3.

112 Maps A surveyor wants to find the distance RS across the lake. He constructs PQT similar to PRS and measures the distances as shown. What is the distance across the lake?

113 Write a proportion. Substitution Find the cross products. Simplify. Divide each side by 25. Answer: The distance across the lake is 28.8 meters.

114 Maps In the figure, MNO is similar to OPQ. Find the distance across the park. Answer: The distance across the park is 4.8 miles.

115 Landmarks Suppose the John Hancock Center in Chicago, Illinois, casts a foot shadow at the same time a nearby tourist casts a 1.5-foot shadow. If the tourist is 6 feet tall, how tall is the John Hancock Center? Explore Plan Solve You know the lengths of the shadows and the height of the tourist. You need to find the height of the John Hancock Center. tourist s shadow Write and solve a proportion. tourist s height building s shadow building s height

116 Find the cross products. Multiply. Divide each side by 1.5. Answer: The height of the John Hancock Center is 1030 feet.

117 Building A man standing near a building casts a 2.5-foot shadow at the same time the building casts a 200-foot shadow. If the man is 6 feet tall, how tall is the building? Answer: The height of the building is 480 feet.

118

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

120 Example 1 Find Trigonometric Ratios Example 2 Use a Calculator to Find Trigonometric Ratios Example 3 Use Trigonometric Ratios Example 4 Use Trigonometric Ratios to Solve a Problem

121 Find sin A, cos A, and tan A. Answer:

122 Find sin A, cos A, and tan A. Answer:

123 Find sin A, cos A, and tan A. Answer:

124 Find sin B, cos B, and tan B. Answer: sin B = 0.8; cos B = 0.6; tan B =

125 Find the value of sin 19 to the nearest ten thousandth. SIN 19 ENTER Answer: sin 19 is about

126 Find the value of cos 51 to the nearest ten thousandth. COS 51 ENTER Answer: cos 51 is about

127 Find the value of tan 24 to the nearest ten thousandth. TAN 24 ENTER Answer: tan 24 is about

128 Find each value to the nearest ten thousandth. a. sin 63 b. cos 14 c. tan 41 Answer: Answer: Answer:

129 Find the missing measure. Round to the nearest tenth. The measures of an acute angle and the side adjacent to it are known. You need to find the measure of the hypotenuse. Use the cosine ratio. Write the cosine ratio.

130 Substitution Multiply each side by x. Simplify. Divide each side by cos 71.

131 12 COS 71 ENTER Simplify. Answer: The measure of the hypotenuse is about 36.9 units.

132 Find the missing measure. Round to the nearest tenth. Answer: The measure of the missing side is about 21.4 units.

133 Architecture A tourist visiting the Petronas Towers in Kuala Lumpur, Malaysia, stands 261 feet away from their base. She looks at the top at an angle of 80 with the ground. How tall are the Towers? Use the tangent ratio. Write the tangent ratio.

134 Substitution Multiply each side by X TAN 80 ENTER Simplify. Answer: The height of the Towers is about feet.

135 Architecture Jenna stands 142 feet away from the base of a building. She looks at the top at an angle of 62 with the ground. How tall is the building? Answer: The building is about feet tall.

136

137 Explore online information about the information introduced in this chapter. Click on the Connect button to launch your browser and go to the Pre-Algebra Web site. At this site, you will find extra examples for each lesson in the Student Edition of your textbook. When you finish exploring, exit the browser program to return to this presentation. If you experience difficulty connecting to the Web site, manually launch your Web browser and go to

138

### Pre-Algebra Interactive Chalkboard Copyright by The McGraw-Hill Companies, Inc. Send all inquiries to:

Pre-Algebra Interactive Chalkboard Copyright by The McGraw-Hill Companies, Inc. Send all inquiries to: GLENCOE DIVISION Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240 Click the mouse button

### as a fraction and as a decimal to the nearest hundredth.

Express each ratio as a fraction and as a decimal to the nearest hundredth. 1. sin A The sine of an angle is defined as the ratio of the opposite side to the hypotenuse. So, 2. tan C The tangent of an

### Name Period Right Triangles and Trigonometry Section 9.1 Similar right Triangles

Name Period CHAPTER 9 Right Triangles and Trigonometry Section 9.1 Similar right Triangles Objectives: Solve problems involving similar right triangles. Use a geometric mean to solve problems. Ex. 1 Use

### Solve each right triangle. Round side measures to the nearest tenth and angle measures to the nearest degree.

Solve each right triangle. Round side measures to the nearest tenth and angle measures to the nearest degree. 42. The sum of the measures of the angles of a triangle is 180. Therefore, The sine of an angle

### Unit 7: Right Triangles and Trigonometry Lesson 7.1 Use Inequalities in a Triangle Lesson 5.5 from textbook

Unit 7: Right Triangles and Trigonometry Lesson 7.1 Use Inequalities in a Triangle Lesson 5.5 from textbook Objectives Use the triangle measurements to decide which side is longest and which angle is largest.

### Right Triangle Trigonometry Test Review

Class: Date: Right Triangle Trigonometry Test Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the length of the missing side. Leave your answer

### Pythagorean Theorem: 9. x 2 2

Geometry Chapter 8 - Right Triangles.7 Notes on Right s Given: any 3 sides of a Prove: the is acute, obtuse, or right (hint: use the converse of Pythagorean Theorem) If the (longest side) 2 > (side) 2

### Types of Angles acute right obtuse straight Types of Triangles acute right obtuse hypotenuse legs

MTH 065 Class Notes Lecture 18 (4.5 and 4.6) Lesson 4.5: Triangles and the Pythagorean Theorem Types of Triangles Triangles can be classified either by their sides or by their angles. Types of Angles An

### Pre-Algebra Interactive Chalkboard Copyright by The McGraw-Hill Companies, Inc. Send all inquiries to:

Pre-Algebra Interactive Chalkboard Copyright by The McGraw-Hill Companies, Inc. Send all inquiries to: GLENCOE DIVISION Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240 Click the mouse button

### Right Triangles Test Review

Class: Date: Right Triangles Test Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the length of the missing side. The triangle is not drawn

### You can solve a right triangle if you know either of the following: Two side lengths One side length and one acute angle measure

Solving a Right Triangle A trigonometric ratio is a ratio of the lengths of two sides of a right triangle. Every right triangle has one right angle, two acute angles, one hypotenuse, and two legs. To solve

### Geometry: Classifying, Identifying, and Constructing Triangles

Geometry: Classifying, Identifying, and Constructing Triangles Lesson Objectives Teacher's Notes Lesson Notes 1) Identify acute, right, and obtuse triangles. 2) Identify scalene, isosceles, equilateral

### 7.1 Apply the Pythagorean Theorem

7.1 Apply the Pythagorean Theorem Obj.: Find side lengths in right triangles. Key Vocabulary Pythagorean triple - A Pythagorean triple is a set of three positive integers a, b, and c that satisfy the equation

### Chapter 8. Right Triangles

Chapter 8 Right Triangles 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 apply the

### Unit 2: Right Triangle Trigonometry RIGHT TRIANGLE RELATIONSHIPS

Unit 2: Right Triangle Trigonometry This unit investigates the properties of right triangles. The trigonometric ratios sine, cosine, and tangent along with the Pythagorean Theorem are used to solve right

### UNIT 8 RIGHT TRIANGLES NAME PER. I can define, identify and illustrate the following terms

UNIT 8 RIGHT TRIANGLES NAME PER I can define, identify and illustrate the following terms leg of a right triangle short leg long leg radical square root hypotenuse Pythagorean theorem Special Right Triangles

### 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

### G E O M E T R Y CHAPTER 9 RIGHT TRIANGLES AND TRIGONOMETRY. Notes & Study Guide

G E O M E T R Y CHAPTER 9 RIGHT TRIANGLES AND TRIGONOMETRY Notes & Study Guide 2 TABLE OF CONTENTS SIMILAR RIGHT TRIANGLES... 3 THE PYTHAGOREAN THEOREM... 4 SPECIAL RIGHT TRIANGLES... 5 TRIGONOMETRIC RATIOS...

### How do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left.

The verbal answers to all of the following questions should be memorized before completion of pre-algebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics

### Solution Guide for Chapter 6: The Geometry of Right Triangles

Solution Guide for Chapter 6: The Geometry of Right Triangles 6. THE THEOREM OF PYTHAGORAS E-. Another demonstration: (a) Each triangle has area ( ). ab, so the sum of the areas of the triangles is 4 ab

### Geometry Notes RIGHT TRIANGLE TRIGONOMETRY

Right Triangle Trigonometry Page 1 of 15 RIGHT TRIANGLE TRIGONOMETRY Objectives: After completing this section, you should be able to do the following: Calculate the lengths of sides and angles of a right

### Give an expression that generates all angles coterminal with the given angle. Let n represent any integer. 9) 179

Trigonometry Chapters 1 & 2 Test 1 Name Provide an appropriate response. 1) Find the supplement of an angle whose measure is 7. Find the measure of each angle in the problem. 2) Perform the calculation.

### Trigonometry (Chapters 4 5) Sample Test #1 First, a couple of things to help out:

First, a couple of things to help out: Page 1 of 24 Use periodic properties of the trigonometric functions to find the exact value of the expression. 1. cos 2. sin cos sin 2cos 4sin 3. cot cot 2 cot Sin

### Right Triangles and SOHCAHTOA: Finding the Measure of an Angle Given any Two Sides (ONLY for ACUTE TRIANGLES Why?)

Name Period Date Right Triangles and SOHCAHTOA: Finding the Measure of an Angle Given any Two Sides (ONLY for ACUTE TRIANGLES Why?) Preliminary Information: SOH CAH TOA is an acronym to represent the following

### 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:

### Section 7.1 Solving Right Triangles

Section 7.1 Solving Right Triangles Note that a calculator will be needed for most of the problems we will do in class. Test problems will involve angles for which no calculator is needed (e.g., 30, 45,

### Square Roots and the Pythagorean Theorem

4.8 Square Roots and the Pythagorean Theorem 4.8 OBJECTIVES 1. Find the square root of a perfect square 2. Use the Pythagorean theorem to find the length of a missing side of a right triangle 3. Approximate

### 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

### 9 Right Triangle Trigonometry

www.ck12.org CHAPTER 9 Right Triangle Trigonometry Chapter Outline 9.1 THE PYTHAGOREAN THEOREM 9.2 CONVERSE OF THE PYTHAGOREAN THEOREM 9.3 USING SIMILAR RIGHT TRIANGLES 9.4 SPECIAL RIGHT TRIANGLES 9.5

### Pre-Algebra Interactive Chalkboard Copyright by The McGraw-Hill Companies, Inc. Send all inquiries to:

Pre-Algebra Interactive Chalkboard Copyright by The McGraw-Hill Companies, Inc. Send all inquiries to: GLENCOE DIVISION Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240 Lesson 5-1 Lesson 5-2

### Intermediate Algebra with Trigonometry. J. Avery 4/99 (last revised 11/03)

Intermediate lgebra with Trigonometry J. very 4/99 (last revised 11/0) TOPIC PGE TRIGONOMETRIC FUNCTIONS OF CUTE NGLES.................. SPECIL TRINGLES............................................ 6 FINDING

### 11 Trigonometric Functions of Acute Angles

Arkansas Tech University MATH 10: Trigonometry Dr. Marcel B. Finan 11 Trigonometric Functions of Acute Angles In this section you will learn (1) how to find the trigonometric functions using right triangles,

### Any two right triangles, with one other angle congruent, are similar by AA Similarity. This means that their side lengths are.

Lesson 1 Trigonometric Functions 1. I CAN state the trig ratios of a right triangle 2. I CAN explain why any right triangle yields the same trig values 3. I CAN explain the relationship of sine and cosine

### Unit 10: Quadratic Equations Chapter Test

Unit 10: Quadratic Equations Chapter Test Part 1: Multiple Choice. Circle the correct answer. 1. The area of a square is 169 cm 2. What is the length of one side of the square? A. 84.5 cm C. 42.25 cm B.

### Trigonometry. Week 1 Right Triangle Trigonometry

Trigonometry Introduction Trigonometry is the study of triangle measurement, but it has expanded far beyond that. It is not an independent subject of mathematics. In fact, it depends on your knowledge

### 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.

### Lesson 19. Triangle Properties. Objectives

Student Name: Date: Contact Person Name: Phone Number: Lesson 19 Triangle Properties Objectives Understand the definition of a triangle Distinguish between different types of triangles Use the Pythagorean

### 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

### Geometry review There are 2 restaurants in River City located at map points (2, 5) and (2, 9).

Geometry review 2 Name: ate: 1. There are 2 restaurants in River City located at map points (2, 5) and (2, 9). 2. Aleta was completing a puzzle picture by connecting ordered pairs of points. Her next point

### Pythagorean Theorem & Trigonometric Ratios

Algebra 2012-2013 Pythagorean Theorem & Trigonometric Ratios Name: Teacher: Pd: Table of Contents DAY 1: SWBAT: Calculate the length of a side a right triangle using the Pythagorean Theorem Pgs: 1-4 HW:

### Created by Ethan Fahy

Created by Ethan Fahy To proceed to the next slide click the button. Next NCTM: Use trigonometric relationships to determine lengths and angle measures. NCTM: Use geometric ideas to solve problems in,

### MA Lesson 19 Summer 2016 Angles and Trigonometric Functions

DEFINITIONS: An angle is defined as the set of points determined by two rays, or half-lines, l 1 and l having the same end point O. An angle can also be considered as two finite line segments with a common

### Express each ratio as a fraction and as a decimal to the nearest hundredth.

Express each ratio as a fraction and as a decimal to the nearest hundredth. 1.sin A SOLUTION: The sine of an angle is defined as the ratio of the opposite side to the hypotenuse. So, ANSWER: 2.tan C SOLUTION:

### Law of Cosines. If the included angle is a right angle then the Law of Cosines is the same as the Pythagorean Theorem.

Law of Cosines In the previous section, we learned how the Law of Sines could be used to solve oblique triangles in three different situations () where a side and two angles (SAA) were known, () where

### Chapter 8 Geometry We will discuss following concepts in this chapter.

Mat College Mathematics Updated on Nov 5, 009 Chapter 8 Geometry We will discuss following concepts in this chapter. Two Dimensional Geometry: Straight lines (parallel and perpendicular), Rays, Angles

### Mid-Chapter Quiz: Lessons 4-1 through 4-4

Find the exact values of the six trigonometric functions of θ. Find the value of x. Round to the nearest tenth if necessary. 1. The length of the side opposite is 24, the length of the side adjacent to

### Similarity, Right Triangles, and Trigonometry

Instruction Goal: To provide opportunities for students to develop concepts and skills related to trigonometric ratios for right triangles and angles of elevation and depression Common Core Standards Congruence

### http://www.castlelearning.com/review/teacher/assignmentprinting.aspx 5. 2 6. 2 1. 10 3. 70 2. 55 4. 180 7. 2 8. 4

of 9 1/28/2013 8:32 PM Teacher: Mr. Sime Name: 2 What is the slope of the graph of the equation y = 2x? 5. 2 If the ratio of the measures of corresponding sides of two similar triangles is 4:9, then the

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

Name: Class: Date: ID: A Q3 Geometry Review Multiple Choice Identify the choice that best completes the statement or answers the question. Graph the image of each figure under a translation by the given

### Each pair of opposite sides of a parallelogram is congruent to each other.

Find the perimeter and area of each parallelogram or triangle. Round to the nearest tenth if necessary. 1. Use the Pythagorean Theorem to find the height h, of the parallelogram. 2. Each pair of opposite

### The Pythagorean Packet Everything Pythagorean Theorem

Name Date The Pythagorean Packet Everything Pythagorean Theorem Directions: Fill in each blank for the right triangle by using the words in the Vocab Bo. A Right Triangle These sides are called the of

### 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:,

### Similar Right Triangles

9.1 Similar Right Triangles Goals p Solve problems involving similar right triangles formed b the altitude drawn to the hpotenuse of a right triangle. p Use a geometric mean to solve problems. THEOREM

### Right Triangle Trigonometry

Right Triangle Trigonometry Lori Jordan, (LoriJ) Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) To access a customizable version of this book, as well as other interactive

### 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

### FLC Ch 1 & 3.1. A ray AB, denoted, is the union of and all points on such that is between and. The endpoint of the ray AB is A.

Math 335 Trigonometry Sec 1.1: Angles Definitions A line is an infinite set of points where between any two points, there is another point on the line that lies between them. Line AB, A line segment is

### 11-1 Areas of Parallelograms and Triangles. Find the perimeter and area of each parallelogram or triangle. Round to the nearest tenth if necessary.

Find the perimeter and area of each parallelogram or triangle. Round to the nearest tenth if necessary. 2. 1. Use the Pythagorean Theorem to find the height h, of the parallelogram. Each pair of opposite

### Free Pre-Algebra Lesson 55! page 1

Free Pre-Algebra Lesson 55! page 1 Lesson 55 Perimeter Problems with Related Variables Take your skill at word problems to a new level in this section. All the problems are the same type, so that you can

### Right Triangles and SOHCAHTOA: Finding the Length of a Side Given One Side and One Angle

Right Triangles and SOHCAHTOA: Finding the Length of a Side Given One Side and One Angle Preliminar Information: is an acronm to represent the following three trigonometric ratios or formulas: opposite

### 10-4 Angles of Elevation and Depression. Do Now Lesson Presentation Exit Ticket

Do Now Lesson Presentation Exit Ticket Do Now #15 1. Identify the pairs of alternate interior angles. 2 and 7; 3 and 6 2. Use your calculator to find tan 30 to the nearest hundredth. 0.58 3. Solve. Round

### (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

### 4.1 Converse of the Pyth TH and Special Right Triangles

Name Per 4.1 Converse of the Pyth TH and Special Right Triangles CONVERSE OF THE PYTHGOREN THEOREM Can be used to check if a figure is a right triangle. If triangle., then BC is a Eample 1: Tell whether

### Right Triangles Long-Term Memory Review Review 1

Review 1 1. Is the statement true or false? If it is false, rewrite it to make it true. A right triangle has two acute angles. 2 2. The Pythagorean Theorem for the triangle shown would be a b c. Fill in

### 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

### MATH 10 COMMON TRIGONOMETRY CHAPTER 2. is always opposite side b.

MATH 10 OMMON TRIGONOMETRY HAPTER 2 (11 Days) Day 1 Introduction to the Tangent Ratio Review: How to set up your triangles: Angles are always upper case ( A,, etc.) and sides are always lower case (a,b,c).

### RIGHT TRIANGLE TRIGONOMETRY

RIGHT TRIANGLE TRIGONOMETRY The word Trigonometry can be broken into the parts Tri, gon, and metry, which means Three angle measurement, or equivalently Triangle measurement. Throughout this unit, we will

### THE DISTANCE FORMULA

THE DISTANCE FORMULA In this activity, you will develop a formula for calculating the distance between any two points in a coordinate plane. Part 1: Distance Along a Horizontal or Vertical Line To find

### Geometry, Final Review Packet

Name: Geometry, Final Review Packet I. Vocabulary match each word on the left to its definition on the right. Word Letter Definition Acute angle A. Meeting at a point Angle bisector B. An angle with a

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. A) 110 B) 120 C) 60 D) 150

Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Convert the angle to decimal degrees and round to the nearest hundredth of a degree. ) 56

### 9-1 Similar Right Triangles (Day 1) 1. Review:

9-1 Similar Right Triangles (Day 1) 1. Review: Given: ACB is right and AB CD Prove: ΔADC ~ ΔACB ~ ΔCDB. Statement Reason 2. In the diagram in #1, suppose AD = 27 and BD = 3. Find CD. (You may find it helps

### EXPONENTS. To the applicant: KEY WORDS AND CONVERTING WORDS TO EQUATIONS

To the applicant: The following information will help you review math that is included in the Paraprofessional written examination for the Conejo Valley Unified School District. The Education Code requires

### Looking for Pythagoras: Homework Examples from ACE

Looking for Pythagoras: Homework Examples from ACE Investigation 1: Coordinate Grids, ACE #20, #37 Investigation 2: Squaring Off, ACE #16, #44, #65 Investigation 3: The Pythagorean Theorem, ACE #2, #9,

### 8-2 The Pythagorean Theorem and Its Converse. Find x.

Find x. 1. of the hypotenuse. The length of the hypotenuse is 13 and the lengths of the legs are 5 and x. 2. of the hypotenuse. The length of the hypotenuse is x and the lengths of the legs are 8 and 12.

### 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

### 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

### Right Triangles A right triangle, as the one shown in Figure 5, is a triangle that has one angle measuring

Page 1 9 Trigonometry of Right Triangles Right Triangles A right triangle, as the one shown in Figure 5, is a triangle that has one angle measuring 90. The side opposite to the right angle is the longest

### 1 Math 116 Supplemental Textbook (Pythagorean Theorem)

1 Math 116 Supplemental Textbook (Pythagorean Theorem) 1.1 Pythagorean Theorem 1.1.1 Right Triangles Before we begin to study the Pythagorean Theorem, let s discuss some facts about right triangles. The

### Introduction Assignment

PRE-CALCULUS 11 Introduction Assignment Welcome to PREC 11! This assignment will help you review some topics from a previous math course and introduce you to some of the topics that you ll be studying

### CHAPTER 8: ACUTE TRIANGLE TRIGONOMETRY

CHAPTER 8: ACUTE TRIANGLE TRIGONOMETRY Specific Expectations Addressed in the Chapter Explore the development of the sine law within acute triangles (e.g., use dynamic geometry software to determine that

### Law of Sines. Definition of the Law of Sines:

Law of Sines So far we have been using the trigonometric functions to solve right triangles. However, what happens when the triangle does not have a right angle? When solving oblique triangles we cannot

### Instructions for SA Completion

Instructions for SA Completion 1- Take notes on these Pythagorean Theorem Course Materials then do and check the associated practice questions for an explanation on how to do the Pythagorean Theorem Substantive

### 4-1 Right Triangle Trigonometry

Find the exact values of the six trigonometric functions of θ. 1. The length of the side opposite θ is 8 is 18., the length of the side adjacent to θ is 14, and the length of the hypotenuse 3. The length

### Unit 7 - Test. Name: Class: Date: 1. If BCDE is congruent to OPQR, then DE is congruent to?. A. PQ B. OR C. OP D. QR 2. BAC?

Class: Date: Unit 7 - Test 1. If BCDE is congruent to OPQR, then DE is congruent to?. A. PQ B. OR C. OP D. QR 2. BAC? A. PNM B. NPM C. NMP D. MNP 3. Given QRS TUV, QS = 3v + 2, and TV = 7v 6, find the

### Quick Reference ebook

This file is distributed FREE OF CHARGE by the publisher Quick Reference Handbooks and the author. Quick Reference ebook Click on Contents or Index in the left panel to locate a topic. The math facts listed

### 4-1 Right Triangle Trigonometry

Find the measure of angle θ. Round to the nearest degree, if necessary. 31. Because the lengths of the sides opposite θ and the hypotenuse are given, the sine function can be used to find θ. 35. Because

### Functions - Inverse Trigonometry

10.9 Functions - Inverse Trigonometry We used a special function, one of the trig functions, to take an angle of a triangle and find the side length. Here we will do the opposite, take the side lengths

### Who uses this? Engineers can use angles measured in radians when designing machinery used to train astronauts. (See Example 4.)

1- The Unit Circle Objectives Convert angle measures between degrees and radians. Find the values of trigonometric functions on the unit circle. Vocabulary radian unit circle California Standards Preview

# 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

### a c Pythagorean Theorem: a 2 + b 2 = c 2

Section 2.1: The Pythagorean Theorem The Pythagorean Theorem is a formula that gives a relationship between the sides of a right triangle The Pythagorean Theorem only applies to RIGHT triangles. A RIGHT

### 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

### ALGEBRA 2/ TRIGONOMETRY

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA 2/ TRIGONOMETRY Friday, June 14, 2013 1:15 4:15 p.m. SAMPLE RESPONSE SET Table of Contents Practice Papers Question 28.......................

### 8-1 Geometric Mean. or Find the geometric mean between each pair of numbers and 20. similar triangles in the figure.

8-1 Geometric Mean or 24.5 Find the geometric mean between each pair of numbers. 1. 5 and 20 4. Write a similarity statement identifying the three similar triangles in the figure. numbers a and b is given

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 29, :15 a.m. SAMPLE RESPONSE SET

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, January 29, 2014 9:15 a.m. SAMPLE RESPONSE SET Table of Contents Question 29................... 2 Question 30...................

### Whole Numbers and Integers (44 topics, no due date)

Course Name: PreAlgebra into Algebra Summer Hwk Course Code: GHMKU-KPMR9 ALEKS Course: Pre-Algebra Instructor: Ms. Rhame Course Dates: Begin: 05/30/2015 End: 12/31/2015 Course Content: 302 topics Whole

### Answer Key. Lesson 7.1. Study Guide

Answer Key Lesson 7.1 Study Guide 1. leg; 30 2. hypotenuse; 3 Ï } 13 3. hypotenuse; 52 4. leg; 20 Ï } 6 5. leg; 5 Ï } 3 6. hypotenuse; 39 7. 1452 yd 2 8. 540 mi 2 9. 5, 12, 13; 130 cm 10. 7, 24, 25; 96

### 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

### 6) Which of the following is closest to the length of the diagonal of a square that has sides that are 60 feet long?

1) The top of an 18-foot ladder touches the side of a building 14 feet above the ground. Approximately how far from the base of the building should the bottom of the ladder be placed? 4.0 feet 8.0 feet