[PDF] [PDF] Special Right Triangles - Study Guide and Intervention

[PDF] 8-1 Study Guide and Intervention - MRS FRUGE

Glencoe Precalculus 8-1 Study Guide and Intervention Introduction to Vectors Geometric Vectors A vector is a quantity that has both magnitude and direction

[PDF] 2019-01-08 13:58

8 jan 2019 · 7-5 Study Guide and Intervention Introduction to Vectors Geometric Vectors A vector is a quantity that has both magnitude and direction

[PDF] Study Guide and Intervention Vectors

Magnitude and Direction A vector is a directed segment representing a Algebra : Concepts and Applications Answers Study Guide and Intervention V ectors

[PDF] PC 8-1 Keypdf - Edinburg CUSD 

Introduction to Vectors Use a ruler and a protractor to draw an arrow diagram for each quantity described Include a scale on each diagram 1 r= 60 meters at a 

[PDF] Study Guide and Intervention Workbook - Metrolina Regional

5 déc 2018 · completed Study Guide and Intervention Workbook can help you in answers to these worksheets are available at the end of each Chapter 8-7 Vectors Identify the hypothesis and conclusion of the conditional statement

[PDF] Chapter 9 Packetpdf

9-6 Vectors Component

[PDF] Chapter 8 Resource Masters

25 août 2014 · Study Guide, Practice, and Enrichment masters and printing in the Advanced Mathematical Concepts TeacherWorks CD-ROM The Fast File 

[PDF] Study Guide and Intervention - New Lexington Schools

Study Guide and Intervention (continued) Variables Find the solution of each equation if the replacement sets are X , , 1, 2, 3 hypothesis and conclusion of

[PDF] Special Right Triangles - Study Guide and Intervention

In a 45°-45°-90° right triangle the hypotenuse is √ 2 times the leg If the hypotenuse is 6 units, find the length of each leg The hypotenuse is √ 2 times the leg, so

[PDF] 8 1 study guide and intervention midpoint and distance formulas answers

[PDF] 8 1 study guide and intervention monomials and factoring

[PDF] 8 1 study guide and intervention multiplying monomials

[PDF] 8 2 factoring using the distributive property

[PDF] 8 2 practice adding and subtracting polynomials

[PDF] 8 2 practice factoring using the distributive property

[PDF] 8 2 practice multiplying a polynomial by a monomial

[PDF] 8 2 practice multiplying and factoring form g

[PDF] 8 2 skills practice adding and subtracting polynomials

[PDF] 8 2 skills practice adding and subtracting rational expressions

[PDF] 8 2 skills practice adding and subtracting rational expressions answers

[PDF] 8 2 skills practice dividing monomials

[PDF] 8 2 skills practice multiplying a polynomial by a monomial answer key

[PDF] 8 2 skills practice multiplying a polynomial by a monomial answers

[PDF] 8 2 skills practice multiplying a polynomial by a monomial answers with work

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Compan ies, Inc.

NAME DATE PERIOD

Chapter 8 18 Glencoe Geometry

Study Guide and Intervention

Special Right Triangles

Properties of 45°-45°-90° Triangles The sides of a 45°-45°-90° right triangle have a

special relationship.

If the leg of a 45°-45°-90°

right triangle is x units, show that the hypotenuse is x ⎷ ?

2 units.

x⎷‾ xx

245°

45

Using the Pythagorean Theorem with

a = b = x, then c 2 = a 2 + b 2 c 2 = x 2 + x 2 c2 = 2x 2 c = 2x 2 c = x ⎷ ? 2 In a 45°-45°-90° right triangle the hypotenuse is

2 times

the leg. If the hypotenuse is 6 units, find the length of each leg.

The hypotenuse is

⎷ ? 2 times the leg, so divide the length of the hypotenuse by ⎷ ? 2 . a 6 ⎷ ? 2 6 ⎷ ? 2 ⎷ ? 2 ⎷ ? 2 6 2 ? 2 = 3 ⎷ ? 2 units

Exercises

Find x.

1. x

845°

45
2. x45°

3⎷‾2 3.

45°4

x 4. xx 18 5.

45°16

xx 6.

45°24

x 2

7. If a 45°-45°-90° triangle has a hypotenuse length of 12, find t

he leg length.

8. Determine the length of the leg of 45°-45°-90° triangle with a

hypotenuse length of

25 inches.

9. Find the length of the hypotenuse of a 45°-45°-90° triangle wit

h a leg length of 14 centimeters.8-3

Example 1Example 2

9

2 ≈ 12.7 8

2 ≈ 11.3 24 8 ⎷ ?

2 ≈ 11.3 3 4

2 ≈ 5.7

6

2 ≈ 8.5

25
2 2 in. ≈ 17.7 in. 14

2 cm ≈ 19.8 cm

Lesson 8-3

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Compan ies, Inc.

NAME DATE PERIOD

Chapter 8 19 Glencoe Geometry

Study Guide and Intervention (continued)

Special Right Triangles

Properties of 30°-60°-90° Triangles The sides of a 30°-60°-90° right triangle also have a special relationship. In a 30°-60°-90° right triangle the hypotenuse is twice the shorter leg. Show that the longer leg is

3 times

the shorter leg. ? MNQ is a 30°-60°-90° right triangle, and the length of the hypotenuse

MN is two times the length of the shorter side

NQ .

Use the Pythagorean Theorem.

a 2 = (2x) 2 - x 2 a 2 = c 2 - b 2 a 2 = 4x 2 - x 2

Multiply.

a 2 = 3x 2

Subtract.

a = 3x 2

Take the positive square root of each side.

a = x ⎷ ? 3 Simplify. In a 30°-60°-90° right triangle, the hypotenuse is 5 centimeter s. Find the lengths of the other two sides of the triangle. If the hypotenuse of a 30°-60°-90° right triangle is 5 centimet ers, then the length of the shorter leg is one-half of 5, or 2.5 centimeters. The length of the long er leg is ⎷ ? 3 times the length of the shorter leg, or (2.5)( ⎷ ? 3 ) centimeters.

Exercises

Find x and y.

1. x y 30

°60°

1 2 2. xy 60
8 3. x y 11 30
4. xy 30
9 ⎷‾3 5. xy 60
12 6.

60°

x20 y

7. An equilateral triangle has an altitude length of 36 feet. Determine the

length of a side of the triangle.

8. Find the length of the side of an equilateral triangle that has an altit

ude length of 45 centimeters. 8-3

30°

60°x2xa

Example 1

Example 2

x = 1; x = 8

3 ≈ 13.9; x = 5.5;

y = 0.5

3 ≈ 0.9 y = 16 y = 5.5

3 ≈ 9.5

x = 9; x = 4

3 ≈ 6.9; x = 10

3 ≈ 17.3;

y = 18 y = 8

3 ≈ 13.9 y = 10

24

3 feet ≈ 41.6 ft

30

3 cm ≈ 52 cm

quotesdbs_dbs17.pdfusesText_23