Name ________________________________________ Date ___________________ Class __________________ Chapter
5
Properties and Attributes of Triangles Chapter Test Form C
1. In �ABC, B is on the perpendicular bisector of AC , m∠A = (6x + 14)�, and m∠ABC = (10x − 2)�. Find m∠C.
6. Find the coordinates of the centroid of the triangle with vertices at (−4, −2), (1, 2), and (6, 3). ________________________________________
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7. Find the coordinates of the orthocenter of �TUV with T(0, 0), U(4, 4), and V(1, 7).
2. Write an equation in point-slope form for the perpendicular bisector of the segment with endpoints (2, 4) and (6, 2).
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8. Find the value of x.
3. Find m∠DEF.
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9. What is m∠TAC?
4. Find the center of the circle circumscribed about the triangle with vertices (0, 0), (8, 0), and (6, 4). _________________________________________
5. TG and GV are angle bisectors of �TUV. Find m∠VGT and the distance from G to UV .
________________________________________
10. Use indirect reasoning to explain why an obtuse triangle cannot have a right angle. ________________________________________ ________________________________________ ________________________________________
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Holt McDougal Geometry
Name ________________________________________ Date ___________________ Class __________________ Chapter
5
Properties and Attributes of Triangles Chapter Test Form C continued
11. The lengths of two sides of a triangle are 7 and 12. Find the range of possible lengths for the third side.
15. Write True or False. Multiplying each number of a Pythagorean triple by a nonzero whole number yields another Pythagorean triple.
_________________________________________ ________________________________________
12. List the angles of �KLM with vertices K(−2, −2), L(2, 6), M(7, −2) in order from smallest to largest.
16. The longest side of a triangle is 13 centimeters. Another side is 11 centimeters. If the triangle is obtuse, write an inequality for the range of values for the third side.
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13. Find the range of values for x. ________________________________________
17. Determine the perimeter of a square with a diagonal of 72 centimeters. ________________________________________
18. Find the area of a 30�-60�-90� triangle with hypotenuse length of 48 inches.
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14. Determine the side lengths of the triangle.
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Holt McDougal Geometry
11. False
Performance Assessment
12. KM, KL, LM
1. Perpendicular Bisector Theorem
13. 6 < x < 10
2. B is the midpoint of AC since BE is a midsegment.
14. 24
3. 90°; Def. of perpendicular bisector
15. The lengths do not form a Pythagorean triple because the hypotenuse ( 34 ) is not a whole number.
4. ∠BDC, ∠DBE, ∠EDB, ∠ABE, ∠A 5. AE < AB; ∠AEB = 90°, ∠ABE = 45°, and, if two angles in a triangle are not congruent, then the longer side is opposite the larger angle.
16. obtuse 17. 6 18. 10
6. The triangles are not congruent. The reasoning in the answer for question 5 can be used to show that AB > AE and AB > EB and likewise that DC > BC. But since AB = BC, it follows that DC is longer than each side of �ABE. Therefore �ABE cannot be congruent to �CDB.
Chapter Test Form C: Free Response
1. 56° 2. y − 3 = 2(x − 4) 3. 72° or 8° ⎛ 1⎞ 4. ⎜ 4, ⎟ ⎝ 2⎠ 5. m∠VGT = 108°; the distance from G to UV = 19.5
7. a. 14 b. 14 2, or about 19.8 c. 28 d. 28 2, or about 39.6
6. (1, 1) 7. (4, 4)
Cumulative Test
8. 4 or −3 9. 132° 10. Let �ABC be an obtuse triangle with ∠A as its obtuse angle. Suppose �ABC has a right angle, say ∠B. Since m∠A > 90° and m∠B = 90°, and since it must be true that m∠C > 0°, it follows that m∠A + m∠B + m∠C > 180°. This last inequality contradicts the Triangle Sum Theorem. The assumption that m∠B = 90° is therefore false. Hence the obtuse triangle cannot have a right angle. 11. 5 < s < 19 12. ∠M, ∠L, ∠K 13. 3 < x < 10 14. 9, 12, and 15 15. True 16. 2 < x < 4 3 17. 24 cm 2
2
18. 288 3 in or about 498.8 in
1. C
20. H
2. F
21. C
3. D
22. G
4. H
23. A
5. A
24. H
6. G
25. B
7. A
26. G
8. J
27. D
9. D
28. H
10. G
29. B
11. C
30. J
12. F
31. B
13. D
32. H
14. G
33. A
15. A
34. H
16. G
35. C
17. D
36. G
18. F
37. B
19. D
38. G
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
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