Chapter 5 Practice Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Find the value of x. The diagram is not to scale.
a. / 32 / b. / 50 / c. / 64 / d. / 80
____ 2. B is the midpoint of D is the midpoint of and AE = 21. Find BD. The diagram is not to scale.
a. / 42 / b. / 21 / c. / 11.5 / d. / 10.5
____ 3. Points B, D, and F are midpoints of the sides of EC = 30 and DF = 23. Find AC. The diagram is not to scale.
a. / 30 / b. / 11.5 / c. / 60 / d. / 46
____ 4. Use the information in the diagram to determine the height of the tree. The diagram is not to scale.
a. / 75 ft / b. / 150 ft / c. / 35.5 ft / d. / 37.5 ft
____ 5. Find the value of x.
a. / 4 / b. / 8 / c. / / d. / 6
____ 6. Find the length of the midsegment. The diagram is not to scale.
a. / 24 / b. / 0 / c. / 42 / d. / 84
____ 7. The length of is shown. What other length can you determine for this diagram?
a. / EF = 12 / c. / DF = 24
b. / DG = 12 / d. / No other length can be determined.
____ 8. Q is equidistant from the sides of Find the value of x. The diagram is not to scale.
a. / 27 / b. / 3 / c. / 15 / d. / 30
____ 9. bisects Find the value of x. The diagram is not to scale.
a. / / b. / 90 / c. / 30 / d. / 6
____ 10. Which statement can you conclude is true from the given information?
Given: is the perpendicular bisector of
a. / AJ = BJ / c. / IJ = JK
b. / is a right angle. / d. / A is the midpoint of .
____ 11. Which statement is not necessarily true?
Given: is the ^ bisector of
a. / DK = KE / c. / K is the midpoint of .
b. / / d. / DJ = DL
____ 12. Q is equidistant from the sides of Find The diagram is not to scale.
a. / 21 / b. / 42 / c. / 4 / d. / 8
____ 13. bisects Find FG. The diagram is not to scale.
a. / 15 / b. / 14 / c. / 19 / d. / 28
____ 14. Find the center of the circle that you can circumscribe about the triangle.
a. / (, ) / b. / (, ) / c. / (–3, ) / d. / (, –2)
____ 15. In DACE, G is the centroid and BE = 9. Find BG and GE.
a. / BG = , GE = / c. /
b. / / d. / BG = , GE =
____ 16. Name a median for
a. / / b. / / c. / / d. /
____ 17. Name the point of concurrency of the angle bisectors.
a. / A / b. / B / c. / C / d. / not shown
____ 18. Find the length of , given that is a median of the triangle and AC = 26.
a. / 13 / c. / 52
b. / 26 / d. / not enough information
____ 19. Which diagram shows a point P an equal distance from points A, B, and C?
a. / / c. /b. / / d. /
____ 20. What is the name of the segment inside the large triangle?
a. / perpendicular bisector / c. / median
b. / altitude / d. / midsegment
____ 21. In centroid D is on median . and Find AM.
a. / 13 / b. / / c. / 12 / d. /____ 22. Name the smallest angle of The diagram is not to scale.
a. /
b. /
c. / Two angles are the same size and smaller than the third.
d. /
____ 23. List the sides in order from shortest to longest. The diagram is not to scale.
a. / / b. / / c. / / d. /
____ 24. Which three lengths could be the lengths of the sides of a triangle?
a. / 12 cm, 5 cm, 17 cm / c. / 9 cm, 22 cm, 11 cmb. / 10 cm, 15 cm, 24 cm / d. / 21 cm, 7 cm, 6 cm
____ 25. Which three lengths can NOT be the lengths of the sides of a triangle?
a. / 23 m, 17 m, 14 m / c. / 5 m, 7 m, 8 mb. / 11 m, 11 m, 12 m / d. / 21 m, 6 m, 10 m
____ 26. Two sides of a triangle have lengths 10 and 18. Which inequalities describe the values that possible lengths for the third side?
a. / / c. / x > 10 and x < 18b. / x > 8 and x < 28 / d. /
____ 27. Two sides of a triangle have lengths 10 and 15. What must be true about the length of the third side, x?
a. / / b. / / c. / / d. /____ 28. and List the sides of in order from shortest to longest.
a. / / b. / / c. / / d. /Short Answer
29. Identify parallel segments in the diagram.
30. B is the midpoint of and D is the midpoint of Solve for x, given and
31. Given: is the perpendicular bisector of IK. Name two lengths that are equal.
32. In draw median FJ from F to the side opposite F.
33. Can these three segments form the sides of a triangle? Explain.
Essay
34. AC and BD are perpendicular bisectors of each other. Find BC, AE, DB, and DC. Justify your answers.
Other
35. T is the midpoint of QR. U is the midpoint of QS. RS = 36 and mÐQUT = 85. What are TU and mÐQSR? Explain.
36. Find EF and DG. For each length, explain your answer. If you cannot determine the length of one or both of the segments, write not enough information.
37. Two sides of a triangle have lengths 6 and 8. What lengths are possible for the third side? Explain.
Chapter 5 Practice Test
Answer Section
MULTIPLE CHOICE
1. ANS: C REF: 5-1 Midsegments of Triangles TOP: 5-1 Example 1
2. ANS: D REF: 5-1 Midsegments of Triangles TOP: 5-1 Example 1
3. ANS: D REF: 5-1 Midsegments of Triangles TOP: 5-1 Example 1
4. ANS: A REF: 5-1 Midsegments of Triangles TOP: 5-1 Example
5. ANS: A REF: 5-1 Midsegments of Triangles
6. ANS: C REF: 5-1 Midsegments of Triangles
7. ANS: A REF: 5-2 Bisectors in Triangles TOP: 5-2 Example 1
8. ANS: B REF: 5-2 Bisectors in Triangles TOP: 5-2 Example 2
9. ANS: D REF: 5-2 Bisectors in Triangle TOP: 5-2 Example 2
10. ANS: C REF: 5-2 Bisectors in Triangles
11. ANS: A REF: 5-2 Bisectors in Triangles
12. ANS: B REF: 5-2 Bisectors in Triangles
OBJ: 5-2.1 Perpendicular Bisectors and Angle Bisectors
STA: CA GEOM 2.0| CA GEOM 4.0| CA GEOM 5.0 TOP: 5-2 Example 2
KEY: Converse of the Angle Bisector Theorem | angle bisector
13. ANS: B REF: 5-2 Bisectors in Triangles TOP: 5-2 Example 2
14. ANS: B REF: 5-3 Concurrent Lines, Medians, and Altitudes TOP: 5-3 Example 1
15. ANS: B REF: 5-3 Concurrent Lines, Medians, and Altitudes TOP: 5-3 Example 3
16. ANS: D REF: 5-3 Concurrent Lines, Medians, and Altitudes TOP: 5-3 Example 4
17. ANS: C REF: 5-3 Concurrent Lines, Medians, and Altitudes
18. ANS: A REF: 5-3 Concurrent Lines, Medians, and Altitudes TOP: 5-3 Example 3
19. ANS: A REF: 5-3 Concurrent Lines, Medians, and Altitudes TOP: 5-3 Example 2
20. ANS: D REF: 5-3 Concurrent Lines, Medians, and Altitudes TOP: 5-3 Example 4
21. ANS: C REF: 5-3 Concurrent Lines, Medians, and Altitudes
22. ANS: D REF: 5-5 Inequalities in Triangles TOP: 5-5 Example 2
23. ANS: C REF: 5-5 Inequalities in Triangles TOP: 5-5 Example 3
24. ANS: B REF: 5-5 Inequalities in Triangles TOP: 5-5 Example 4
25. ANS: D REF: 5-5 Inequalities in Triangles TOP: 5-5 Example 4
26. ANS: B REF: 5-5 Inequalities in Triangles TOP: 5-5 Example 5
27. ANS: A REF: 5-5 Inequalities in Triangles TOP: 5-5 Example 5
28. ANS: A REF: 5-5 Inequalities in Triangles
SHORT ANSWER
29. ANS:
REF: 5-1 Midsegments of Triangles TOP: 5-1 Example 2
30. ANS:
REF: 5-1 Midsegments of Triangles
31. ANS:
IJ and JK
REF: 5-2 Bisectors in Triangles TOP: 5-2 Example 1
32. ANS:
REF: 5-3 Concurrent Lines, Medians, and Altitudes
33. ANS:
No; for three segments to form the sides of a triangle, the sum of the length of two segments must be greater than the length of the third segment.
REF: 5-5 Inequalities in Triangles
ESSAY
34. ANS:
[4] / BC = 13 by the Perpendicular Bisector Theorem.AE = 5 by the Perpendicular Bisector Theorem.
BE = 12 by the Perpendicular Bisector Theorem, so DB = DE + BE = 12 + 12 = 24.
by SAS, so DC = BC = 13.
[3] / finds three lengths with correct explanations
[2] / finds two lengths with correct explanations
[1] / finds one length with correct explanation
REF: 5-2 Bisectors in Triangles
OTHER
35. ANS:
By the Triangle Midsegment Theorem, TU = 18. Also, so mÐQSR = 85 by the Corresponding Angle Postulate.
REF: 5-1 Midsegments of Triangles
36. ANS:
EF: By the definition of perpendicular bisector, EG is the perpendicular bisector of DF. Therefore, by the Perpendicular Bisector Theorem, EF = DE = 6.
DG: not enough information
REF: 5-2 Bisectors in Triangles TOP: 5-2 Example 1
37. ANS:
Let x be the length of the third side. By the Triangle Inequality Theorem,
6 + x > 8, 6 + 8 > x, and 8 + x > 6. Solving each inequality, x > 2, x14, and x–2, respectively, or 2x14.
REF: 5-5 Inequalities in Triangles