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Geometry
Name _______________________________
Chapter 5 pretest
Show work to receive credit!
Date ______________________ Per. ______
It is given that Δ BCD is isosceles with base BD , m  BCD = 78 , m  QBD = 40 , CR bisects
 BCD, and BQ is an altitude. Find the measures of angles 1 through 6.
B
m  1 = _____
m  2 = _____
m  3 = _____
m  4 = _____
m  5 = _____
m  6 = _____
C
2
3
R
6
1
A
Q
5
4
D
7. If CR is a median, BR = 2x – 5, and BD = 3x + 8, find RD.
8. Find the value of x and y so that the triangles are congruent by the indicated reason.
ΔPQR  ΔVSR by HA
P
V
8x - 35
2x - 5
5y
Q
3y + 8
S
R
For problems 9 through 11, use the figure to the right to find each value.
C
9. Name the shortest side of BCD .
60 
D
50 
80 
10. Name the shortest side of ΔABD .
11. Name the shortest segment in
70 
figure ABCD.
60 
A
40 
9. ________________
10. ________________
11. ________________
B
For problems 12 through 15, identify the property that justifies each statement.
12. If m  Y  m  G, then m  Y > m  G.
12. ______________________
13. If x < 15, then 5 + x < 20.
13. ______________________
14. If PQ > RS and RS > 12, then PQ > 12.
14. ______________________
15. If -3x > 12, then x < 4.
15. ______________________
Given A(–5,1), B(–1,4), and C(2,-3)
16. Find the slope of each side.
17. Is  ABC a right triangle?
18. Find the length of each side.
19. Classify  ABC by its sides.
20. The perimeter  ABC of is 84 cm. If AB = 8x – 3, BC = 2x + 12, and AC = 5x, find x and use it to
find the lengths of each side. Use these measures to list the angles in order from largest to smallest.
20. ____________________________
21. Complete the indirect proof below:
Statement: If BD is not the angle bisector of  ABC, then m  1  m  2.
B
Given: BD is not the angle bisector of  ABC
Prove: m  1  m  2
1 2
Assume: _______________________
Work:
A
D
C
This contradicts _______________________
Therefore, _______________________ is false,
so _______________________ must be true.
22. Two sides of a triangle measure 37 and 19 inches. What is the range of values for the third side?
23. Which set of numbers below could be the lengths of the sides of a triangle? Justify your answers.
a) 1,5,6
b) 16,35,18
c) 17,5,14
For problems 24 through 26, name the congruent triangles and state why they are congruent. Use a
regular triangle rule (SSS, SAS, ASA, or AAS), then use a right triangle rule (LL, LA, HA, or HL).
B
C
24.
25.
26. B
C
1
B
A
D
AD CD
D
A
____________________
_________
_________
AD CD
____________________
_________
_________
For problems 27 and 28, write a two-column proof.
27.
28.
G
H
Given: GF  GE
Prove: 1  E
____________________
_________
_________
G
1
1
F
2
A
D
 1 and  2 are right angles
AD  BC
E
C
E
F
H
Given: GE > GF
Prove: 1  E
E