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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. 1008

6. 7.

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)

x

y

2

2

x

y

2

2

x

y

2

2

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

11.

x 8

2x 8 12.

2x 8

3x 8

558

13. x 8

708508

Practice BFor use with the lesson “Apply Triangle Sum Properties”

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Find the measure of the exterior angle shown.

14. x 8

(3x2 22)8

808 15. (4x 1 8)8 (2x 1 3)8

518

16.

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

2x 8

Find the measure of the numbered angle.

17. ∠ 1 18. ∠ 2 12

228

588

208

34

19. ∠ 3 20. ∠ 4

21. In n ABC, m∠ A 5 m∠ B 1 308 and m∠ C 5 m∠ B 1 608. Find the measure of each angle.

22. In n ABC, m∠ A 5 2(m∠ B) and m∠ C 5 3(m∠ B). Find the measure of each angle.

Find the values of x and y.

23.

308

x 8

y 8

24.

398568

508x 8

y 8

25. 708

788748

x 8

y 8

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.

7.14 in.10.5 in.

7.7 in.

Practice B continuedFor use with the lesson “Apply Triangle Sum Properties”

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Lesson Apply Triangle Sum PropertiesTeaching 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. m∠ 1 5 608

16. m∠ 1 5 608; m∠ 2 5 308; m∠ 3 5 808

17. m∠ 1 5 708; m∠ 2 5 658; m∠ 3 5 958

18. m∠ A 5 458; m∠ B 5 908; m∠ C 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.

x

y

2

2

A C

B

9.

B x

y

2

2

C

A

scalene; right triangle scalene; not a right triangle

10.

x

y

2

2

B

C

A

isosceles; not a right triangle

11. 30; right 12. 25; acute 13. 120; acute

14. 1318 15. 1008 16. 1258 17. 368 18. 1228

19. 1228 20. 388 21. m∠ A 5 608, m∠ B 5 308, m∠ C 5 908 22. m∠ A 5 608, m∠ B 5 308, m∠ C 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. m∠ B 5 1158; m∠ C 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. m∠ ABD 5 908, m∠ BDC 5 608 5. m∠ CAB 5 808, m∠ CBA 5 108

Problem Solving Workshop: Worked Out Example

1. The legs are }

RS and }

TS , and the base is } RT ; m∠ 1 5 55°, m∠ 2 5 110°

2. The legs are }

RS and }

TS , and the hypotenuse is } RT ; m∠ SRT 5 54°, m∠ 1 5 144°

Challenge Practice

1. (5, 9) 2. (9, 1)

x

y

A(3, 3)

B(7, 5)

C (5, 9)

x

y

A(3, 3)

D(9, 1)

B(7, 5)

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. m∠ A 5 m∠ 1 8. GIVEN: n ABC PROVE: Sum of exterior angles of n ABC

is 3608.By the definition of a straight angle, you know that m∠ 1 1 m∠ 2 5 1808, m∠ 3 1 m∠ 4 5 1808, and m∠ 5 1 m∠ 6 5 1808. So, it follows that the sum of all six angles is 1808 1 1808 1 1808 5 5408.

Answers for Chapter Congruent Triangles

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