100 758 758 - Geometry

Lesson 4.1

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Date-- ------------------------

Lesson

4.1

Practice B

For use with the lesson "Apply Triangle Sum Properties"

Complete the sentence with always, sometimes, or never. 1. An isosceles triangle is ? a right triangle. 2. An obtuse triangle is ? a right triangle. 3. A right triangle is ? an equilateral triangle. 4. A right triangle is ? an isosceles triangle.

Classify the triangle by its sides and by its angles.

5.

6.

7.

1008

758 758

A triangle has the given vertices. Graph the triangle and classify it by its sides. Then determine if it is a right triangle.

8. A(3, 1), B(3, 4), C(7, 1)

9. A(1, 1), B(4, 0), C(8, 5) 10. A(2, 2), B(6, 2), C(4, 8)

y

y

y

2

2

x

2

2

x

2

2

x

Find the value of x. Then classify the triangle by its angles.

11.

2x 8

12. 3x 8

13. x8

2x 8

558

x8

508

708

Copyright ? Houghton Mifflin Harcourt Publishing Company. All rights reserved.

Geometry

Chapter Resource Book 4-9

Lesson 4.1

Copyright ? Houghton Mifflin Harcourt Publishing Company. All rights reserved.

Name------------------------------------------------

Lesson

4.1

Practice B continued

For use with the lesson "Apply Triangle Sum Properties"

Find the measure of the exterior angle shown.

14. 808

x8

15. (4x 1 8)8 (2x 1 3)8

518

( 3x2 22)8

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16. 2x 8

(103 2 x)8 (6x 2 7)8

Find the measure of the numbered angle.

17. 1

18. 2

19. 3

20. 4

1

228

2

3 588

208

4

21. In nABC, mA 5 mB 1 308 and mC 5 mB 1 608. Find the measure of each angle.

22. In nABC, mA 5 2(mB) and mC 5 3(mB). Find the measure of each angle.

Find the values of x and y.

23.

24.

y8

x8 x8

308

568 398

508

y8

25. 708 x8

748

788

y8

26. Metal Brace The diagram shows the dimensions of a metal brace used for strengthening a vertical and horizontal wooden junction. Classify the triangle formed by its sides. Then copy the triangle, measure the angles, and classify the triangle by its angles.

10.5 in.

7.14 in.

7.7 in.

Geometry

4-10 Chapter Resource Book

answers

Answers for Chapter 4 Congruent Triangles

Lesson 4.1 Apply Triangle Sum Properties

Teaching Guide

1. Check drawings. 2. Check drawings. It is impossible to construct triangles with 3 congruent sides and 1 right angle and with 3 congruent sides and 1 obtuse angle.

Technology Activity

1. The angle measures change; the sum of the angle measures stays the same.

2. Sample answer: 5 triangles; the sum of the angle measures is 1808. 3. The sum of the measures of the angles of any triangle is 1808.

Practice Level A 1. equilateral 2. isosceles 3. scalene 4. isosceles 5. right 6. acute 7. obtuse 8. equiangular 9. 55 10. 35 11. 45 12. 158

13. 90 14. 62 15. m1 5 608 16. m1 5 608; m2 5 308; m3 5 808 17. m1 5 708; m2 5 658; m3 5 958 18. mA 5 458; mB 5 908; mC 5 458 19. scalene; obtuse

Practice Level B

1. sometimes 2. never 3. never 4. sometimes

5. scalene, obtuse 6. scalene, right

7. isosceles, acute

8.

y

9.

y

19. 1228 20. 388 21. mA 5 608, mB 5 308, mC 5 908 22. mA 5 608, mB 5 308, mC 5 908

23. 60, 30 24. 45, 51 25. 24, 66

26. scalene; right

Practice Level C

1. scalene; 20; acute 2. isosceles; 25; acute 3. equilateral; 60; equiangular 4. x 5 10; y 5 71 5. x 5 50; y 5 33 6. x 5 15; y 5 42 7. x 5 85; y 5 58 8. 608 9. 1208 10. 608 11. 1208 12. 308 13. 308 14. 748 15. mB 5 1158; mC 5 238 16. 8 in. by 11 in. by 11 in.; 8 in. by 8 in. by 14 in.

17. 864 in. 18. 576 in. 19. 1344 in.

Study Guide

1. right scalene 2. equiangular equilateral

3. obtuse isosceles 4. mABD 5 908, mBDC 5 608 5. mCAB 5 808, mCBA 5 108

Problem Solving Workshop:

Worked Out Example 1. The legs are } RSand } T S, and the base is } R T;

m1 5 55?, m2 5 110?

2.

Tish} ReTl;egmsarSeR} RTS5an5d4} T?,Sm, and1

the hypotenuse 5 144?

Challenge Practice

1. (5, 9)

2. (9, 1)

y

C (5, 9)

y

B

2A 2

C x

2A 2B

C x

scalene; right trianglescalene; not a right triangle

10.

y

C

isosceles; not a right triangle

2 A 2

B x

11. 30; right 12. 25; acute 13. 120; acute 14. 1318 15. 1008 16. 1258 17. 368 18. 1228

B(7, 5) A(3, 3)

x

A(3, 3)

B(7, 5)

D(9, 1) x

3. 608, 608, 608 4. 638, 368, 818; acute

5. x 5 29, y 5 64 6. x 5 12.9, y 5 51.3

7. mA 5 m1

8. GIVEN: nABC PROVE: S um of exterior angles of nABC is 3608.

By the definition of a straight angle, you know that m1 1 m2 5 1808, m3 1 m4 5 1808, and m5 1 m6 5 1808. So, it follows that the sum of all six angles is 1808 1 1808 1 1808 5 5408.

Copyright ? Houghton Mifflin Harcourt Publishing Company. All rights reserved.

Geometry

Chapter Resource Book A45

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