Answer Key: Medians, Altitudes, Angle Bisectors …



Answer Key: Medians, Altitudes, Angle Bisectors and Perpendicular Bisectors

Worksheet #1: 1. centroid 2. incenter 3. circumcenter 4. centroid, since all 6 triangles have = areas 5. centroid, circumcenter, orthocenter 6. equilateral 7. scalene 8. median 9. altitude, altitude, twice 10. obtuse 11. midpoint of the hypotenuse, vertex of right ( 12. ( bisector, ( 13 ( bisector 14. medians, ( bisectors, and altitudes if the ( is acute 15. the ( bisector is of the base of an isosceles triangle 16. ( bisector 17. ( bisector 18. median, areas are = and median= ½ hypotenuse 19. ( bisectors and lines containing altitudes, medians and angle bisectors 20. ( bisector, ( bisector 21. a. 16 b. 192 c. 64 d. 19.2 e. r= 6

Worksheet #2: 1. 12 2. [pic] 3. 12 4. 9 5. [pic] 6. 9 7. 15 8. 15 9. 15

10. 216 11. 36 12. 54 13. 10 14. 8 15. 18 16. 14.4 17. AC=18 18. 77.76,

138.24 19. 19.2 20. WT=32 21. 138.24, 245.76 22. 12 23. 20 24. 102/3

25. 13 1/3 26. 171/7 27. 22 6/7 28. [pic] 29. [pic] 30. 8

Worksheet #3: 1.AD 2.CF 3.AB 4.EF 5 EF, DF 6.BE 7.CB 8.centroid

9. [pic] 10. [pic] 11. [pic]

Worksheet #4: 1. a. 6 b. 5, 5, 8 c. [pic], [pic] d. 4. [pic] e. 9.6, 2.8

2. a. 48, 12 b. 12, 16 c. 4, 12 3. a. 24 b. 5.25, 18.75 , 8.75

4. 6.72, 1.96, 12.5 5. 3.5, 12, MF = 4 1/6 Area ( = 14 6. 4, 6 7. 5, 11, 6.6

8 a. 9,3 b. 10 c. 6 d. 14.4, 1.2 9 a. 15 b. midpt AB c. 3(5 10 a. 8, 9.6 b. 6

Worksheet #5: 1. 25 2. 25 med = ½ hyp 3. 24 b1 h1=b2 h2 4. 18,32 5. 7 since 32-25=7

6. B 7.M 8. 25 9. 10 10 a. 13 1/3 , 16 2/3 b. 13 1/3 11. 25, 15 b. [pic]

Pythagorean c. 10, center of circle 12. 12 13. 120 / 13 b1 h1 = b2 h2 14. 5,

med= ½ hyp (BEC 15. 3 1/3 16. 2/3 17. 15,17 18. 3 19. 4.8, 10.8

20. a. [pic], [pic], [pic] b. [pic] c. 384 d. 6 ( , or ½ ([pic])([pic])

e. 64, 96, 128, 32

Worksheet #6: 1. a.18 b.15, 15, 24 c. [pic], [pic] d. 12 ,[pic] e. 28.8, 8.4

f. 24 g. 9.6 h. altitude, median, ( bisector 2. a. 432, 108 b. 108, 144 c. 36, 72

d. 72 e. 288 3. a.18 b.11 7/13, 186/13 c. 8,10 d. 6, 24 e. 8 f. 8

4. a. 19.5 b.13 11/13, 36 c. 19.5, 6 d. [pic] 5. 2 :1 ratio 6. altitudes 7. whose

ratio is equal to the remaining sides 8. bh = pr 9. ( bisector 10. ( bisector 11. medians 12. altitudes 13. ( bisectors, obtuse 14. ½ the hypotenuse

15. ( bisectors 16. ( bisectors 17. b1 h1 = b2 h2 18. two tangent segments to the circle

from an outside point are ( 19. altitude, ( bisector, ( bisector 20. isosceles ( vertex (

Worksheet #7: 1. a. 27 b. 22.5, 22.5, 36 (midsegment = ½ side) c. 9, 18 d. [pic], [pic],[pic]

2. a. 43.2, 12.6 b. 36 c. 324 d. 14.4 e. 81 3. a. 972, 243 b. 243, 324 c. 81, 162

d. 162 e. 648 4. a. 27 b. 174/13 , 279/13 c. 12, 15 d. 9, 36 e. 12 f. 12

5. altitudes 6. ( bisectors, medians, altitudes 7. whose ratio equals the ratio of the

remaining two sides 8. ½ the hypotenuse 9.bh = pr 10. ( bisector 11. ½ the

hypotenuse 12. altitude, ( bisector, and median, isosceles, base 13. ( bisectors

14.( bisectors, obtuse 15. congruent 16. ( bisectors 17. ( bisectors 18. bh = bh

19. ( bisector, altitude, and part of the ( bisector 20. = the ratio of remaining sides of (

Worksheet #8: 1. 75, 37.5 2. 37.5 (med= ½ hyp) 3. 36, 27, 48 4. 10.5 5. B, M 6. 37.5, M 7. 15 8. [pic] 8. 20, 25, [pic] 9. 37.5, 22.5, [pic] 10. 3:1, 1:2 11. P, P, P 12. [pic] 13. [pic] 14. [pic] 15. [pic], [pic]

16. (2,5) 17. ( (22, 5 ) ; ( (10, 9 ) ; ( (10, 1 ) 18. [pic], [pic],24 19. [pic]

20. [pic], 8 21. 64 22 a. 192 b. 32 c. 48 d. 64 e. 16 f. 32

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