Download Geometry Review/Test Chapter 5

Geometry Review/Test Chapter 5
Name:_________________
1. Given: CD is the perpendicular bisector of HJ . Which statement is true?
C
H
I
J
D
[A] HCJ is a right angle.
[B] D is the midpoint of HJ
[C] CIJ , JID , DIH , HIC are all right angles.
[D] DJ = CJ
2. Given: A is on the bisector of  BCD, AD  CD, and AB  CB
Prove: A D = A B
D
A
E
C
B
3. Your town is holding local elections. The town sets up three polling stations around the area
that form a triangle. They decide to meet at the circumcenter of their locations. The circumcenter
is equidistant from the three
of the triangle formed by the polling stations.
[A] angles
[B] vertices
[C] sides
[D] angle bisectors
4. NO is the perpendicular bisector of LM . If OM = 4 and LN = 6, then LO =______ and MN
=______. Explain your solutions.
5. In the figure (not drawn to scale), MO bisects LMN , mLMO  15x  21, and
mNMO  x  63. Solve for x and find mLMN .
L
O
M
[A] 6, 138 
[B] 3, 24 
[C] 6, 111 
[D] 3, 27 
N
6. Refer to the figure below.
Given: AF  FC ,  ABE   EBC
A median of  ABC is ____.
[A] GF
[B] BE
[C] BD
[D] BF
7. Refer to figure below.
Given: AF  FC ,  ABE   EBC
An altitude of  ABC is ____.
[A] BD
[B] GF
[C] BF
[D] BE
8. Solve for x given BD = 3x  2 and AE = 4 x  8 . Assume B is the midpoint of AC and D is
the midpoint of CE.
C
B
D
A
E
9. The coordinates of the midpoints of the sides of a triangle are L(0, 1), M(4, 0), and N(2, –2).
Find the coordinates of the vertices of the triangle.
10. Refer to the figure.
The longest side is ______.
[A] NM
[B] LN
[C] MP
[D] ML
11. Which is the appropriate symbol to place in the blank? (not drawn to scale)
AB __ AC
A
17
B
83
2
O
2
C
[A] >
[B] =
[C] <
[D] not enough information
12. Two sides of a triangle have lengths 8 and 11. What are the possible lengths of the third side
x?
13. Write an indirect proof.
Given: m  1 = 122  and m  2 = 121 
Prove: a || b
1
2
a
b
14. Given the triangles below, if ZY  CB , XY  AB , and mB  mY , decide which
statement is true.
X
A
B
Z
Y
C
[A] YZ  BC
[B] XY  AB
[C] XZ  AC
[D] AC  XZ
15. Find the appropriate symbol to place in the blank. (not drawn to scale)
AB __ AC
A
13
B
82
3
O
3
C
Reference: [5.1.1.2]
[1] [C]
Reference: [5.1.2.4]
Statements
Reasons
1. A is on the bisector Given
of  BCD
[2]
AD  CD
AB  CB
2. AD AB
Perpendicular Bisector Theorem
Reference: [5.2.1.5]
[3] [B]
Reference: [5.2.1.6]
[4] LO = 4, MN = 6;  LNO   MNO by SAS, so corresp. parts of congruent triangles are
congruent.
Reference: [5.2.2.19]
[5] [A]
Reference: [5.3.1.27]
[6] [D]
Reference: [5.3.2.36]
[7] [A]
Reference: [5.4.1.40]
[8] 2
Reference: [5.4.2.48]
[9] (–2, –1), (2, 3), (6, –3)
Reference: [5.5.1.51]
[10] [D]
Reference: [5.5.1.52]
[11] [C]
Reference: [5.5.2.58]
[12] 3 < x < 19
Reference: [5.6.1.65]
[13] Assume a || b. If two parallel lines are cut by a transversal, then alternate interior angles are
congruent. This contradicts the given information since m  1  m  2. The assumption that a ||
b is false. Thus a || b .
Reference: [5.6.2.66]
[14] [C]
Reference: [5.6.2.71]
[15] <