Chapter 5 Review
Name ____________________________________ Period ______
suur 1. In the diagram, MN is the perpendicular bisector of AD . What are the values of x and y? M 1 3
5x - 4
x +2 N
A 1 2
4y - 6
y -4
D
suur 2. Given: AB is the perpendicular bisector of IK . What is true?
A
I
J B
suur 3. NO is the perpendicular bisector of LM . If OM = 5 and LN =14, then LO = _____
N
MN = _____
L
M
O
suur 4. In the figure (not drawn to scale), MO bisects RLMN , mRLMO = 7 x +12, and mRNMO =10 x - 6. Solve for x and find mRLMN .
O L
N
M
5. The perpendicular bisectors of V XYZ meet at point P. Find PX.
6. The angle bisectors of V XYZ meet at point P. Find PM.
K
7. Given G is the centroid (where the medians meet) of V ABC and BE = 54. Find B
BG = _____
GE = _____ F
A
8.
Solve for x given BD =
G
D
C
E
3 x + 5 and AE = 8 x + 5 . Assume B is the midpoint of AC and D is 2 C
the midpoint of CE . B
A
9. Use the diagram of V ABC where D, E, and F are the midpoints of the sides. Fill in the blanks: A) AB P _____ B) If AB = 20, then EF = _____ C) If BE = 25, then DF = _____ D) If DE =17, then AC = _____ E) If AB = 4 x + 6 and EF = 3 x + 1, then EF = _____ F) Given AC = 30, DF =11, and AD =18 . Find the Perimeter of VDEF = _______ 10. Does the side lengths 5, 9, and 14 construct a triangle?
C
11. Which is the largest side of V ABC ?
62°
54°
64° A
B
12. Which is the smallest angle of V ABC ?
C
25
A
17
13
B
D
E
13. Two sides of a triangle have lengths 14 and 25. What are the possible lengths of the third side x?
14. Solve the inequality: BC + AC > AB .
A
x + 2
x + 3
B
15. Refer to the figure. What is true about x?
3x - 2
C
x 15 8
60°
75° 8
16. Complete with < , > , or = B) mR1 _____ mR2
A) RS _____ TU S
10
U
92°
1 2
65° R
9
T
17. In VPQR and VEGF , PR @ EF , QR @ GF , PQ = 64 cm, mRF = 85°, and mRR = 75° . Which side length is reasonable for GE ?
a) 64
b) 60
c) 70
d) 54
18. Know definitions for the following: Concurrent Lines, Perpendicular Bisectors of a triangle, Angle Bisectors of a triangle, Medians of a triangle, Altitudes of a triangle, Midsegment of a triangle, Circumcenter, Incenter, Centroid, and Orthocenter.
19. Write the first two lines of this indirect proof. Given: mR1 = 135° and mR2 = 136° . Prove: a P/ b .
a
1 2
Key 9 4 1. x = , y = 7 7
2. IJ = KJ , AB ^ IK
3. LO = 5, MN =14
4. x = 6, mRLMN =108°
5. PX =11
6. PM =13
7. BG = 36, GE =18 8. CE =1 9. A) B) C) D) E) F)
EF EF =10 DF = 25 AC = 34 x = 2, EF = 7 Perimeter of VDEF = 44
10. no
11. CB
12. R C
13. 11 < x < 39
14. x >
1 3
16. A) RS > TU 19.
15. x <15 B) mR1 < mR2
Suppose mR1 = 135° and mR2 = 136° . Prove that a P b .
17. C
b
