1. Concurrent Lines, Medians, and Altitudes
GEOMETRY LESSON 5-3
Pages Exercises
8. C
9. Z
10. Find the bisectors of the sides of the formed by the tennis court, the playground, and the volleyball court. That point will be equidistant from the vertices of the .
11. TY = 18; TW = 27
12. ZY = 4 ; ZU = 13
13. VY = 6; YX = 3
14. Median; A is a midpt.
15. Neither; it’s not a segment drawn from a vertex.
16. Altitude; AB is a segment drawn from a vertex of a perp. to the opp. side. 1 2
1. (–2, –3)
2. (0, 0)
, 1
4. 2, –1
5. –3, 1
6. –3, –4
, 3
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2. Concurrent Lines, Medians, and Altitudes
GEOMETRY LESSON 5-3
17.
18. …
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3. Concurrent Lines, Medians, and Altitudes
GEOMETRY LESSON 5-3
19. BE
20. FC
21. CA
22. DG
23. 1:2 or 2:1
24. Find the circumcenter of the formed by the three pines.
Check student’s work.
bisector; it bisects an .
28. None of these; it is a midsegment
29. Altitude; AB is to a side from a vertex.
30. a. AB
b. BC
c. XC
d. bis.
31. a Bis. Thm.
b Bis. Thm.
c. Trans.
d Bis.
32. a. L(1, 3); M(5, 3);
N(4, 0)
b. AM: y = x;
BN: y = –3x + 12;
CL: y = – + 3 5 3 7 24 7
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4. Concurrent Lines, Medians, and Altitudes
GEOMETRY LESSON 5-3
32. (continued)
c , 2
d. – = – = = 2
e. AM = 34; AP = = ;
BN = = ;
BP = = ; CL = ;
CP = = =
33. I-D; II-B; III-C; IV-A
34. I-A; II-C; III-B; IV-D
35. Answers may vary. Sample: Let ABC be isosc. with base B and C. If AD bisects A, then it is
to BC, and therefore the altitude from A. So, AD contains the circumcenter, incenter, centroid, and orthocenter.
bisectors
37. C 10 3 s 3 7 10 3 24 7 10 7 24 7 14 7
136 9 2 3
160 9 4 3
232 9 2 3
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5. Concurrent Lines, Medians, and Altitudes
GEOMETRY LESSON 5-3
38. H
39. D
40. [2] any acute ; or a list that contains all of the following: equiangular , equilateral , acute isosceles , acute scalene
41. [1] a list that does not contain equiangular ,
40. [1] (continued)
equilateral , acute isosceles , or acute scalene
41. [4] s
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6. Concurrent Lines, Medians, and Altitudes
GEOMETRY LESSON 5-3
41. [4] (continued)
[3] one diagram partially or completely incorrect
[2] two diagrams partially or completely incorrect
[1] three diagrams partially or completely incorrect
42. Yes; TB bisects the .
43. No; point B is equidistant from the sides.
44. No; point B is not necessarily equidistant from the sides.
45. right
46. obtuse
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7. Concurrent Lines, Medians, and Altitudes
GEOMETRY LESSON 5-3
Answers may vary. Samples are given.
47. AB
48. AD
49. ABC and ADE
50. AB and CD
51. BC
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