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Review Chapter 5 - Geometry A
Short Answer
1. Find the value of x. The diagram is not to scale.
32
x
32
27
22
22
2. B is the midpoint of
D is the midpoint of
and AE = 25. Find BD. The diagram is not to scale.
C
B
A
D
E
3. Points B, D, and F are midpoints of the sides of
to scale.
EC = 45 and DF = 22. Find AC. The diagram is not
A
B
F
C
D
E
4. Use the information in the diagram to determine the height of the tree. The diagram is not to scale.
5. Find the value of x.
20
3x – 8
6. Find the length of the midsegment. The diagram is not to scale.
23
26
5x + 4
26
23
4x + 26
7. Q is equidistant from the sides of
Find
The diagram is not to scale.
T
|
(3
x
|
+
4)
°
Q
(4x + 1)°
S
8.
R
bisects
Find FG. The diagram is not to scale.
E
n +5
F
)
3n – 3
)
D
G
9. Find the center of the circle that you can circumscribe about the triangle.
10. In ∆ABC, G is the centroid and BE = 18. Find BG and GE.
C
B
G
A
D
E
F
11. Name a median for
|
C
G
)
|
F
)
E
12. Find the length of
H D
, given that
is a median of the triangle and AC = 22.
D
A
B
C
13. What is the name of the segment inside the large triangle?
14. Name the second largest of the four angles named in the figure (not drawn to scale) if the side included by
and
is 13 cm, the side included by
and
is 10 cm, and the side included by
and
is 17 cm.
1
2
3
4
15. List the sides in order from shortest to longest. The diagram is not to scale.
J
52°
85°
K
43°
L
16.
and
List the sides of
17. Based on the pattern, what are the next two terms of the sequence?
3, 9, 15, 21, . . .
18. Identify the hypothesis and conclusion of this conditional statement:
If today is Wednesday, then tomorrow is Thursday.
19. Line r is parallel to line t. Find m 5. The diagram is not to scale.
r
7
130°
1
t
3
4
2
5
6
20. If BCDE is congruent to OPQR, then
21. Justify the last two steps of the proof.
is congruent to
in order from shortest to longest.
Given:
and
Prove:
P
Q
R
S
Proof:
1.
1. Given
2.
2. Given
3.
4.
3.
4.
22. B is the midpoint of
and D is the midpoint of
Solve for x, given
C
B
A
23. In
D
E
draw median FJ from F to the side opposite F.
and
H
F
G
24. Write the inverse of this statement:
If a figure is a rectangle, then all of its angles are right angles.
25. Can these three segments form the sides of a triangle? Explain.
c
b
a
Review Chapter 5 - Geometry A
Answer Section
SHORT ANSWER
1.
2.
3.
4.
5.
6.
7.
8.
54
12.5
44
50 ft
6
19
13
9
1
9. ( , −2)
2
10.
11.
12. 11
13. median
14.
15.
16.
17. 27, 33
18. Hypothesis: Today is Wednesday. Conclusion: Tomorrow is Thursday.
19. 130
20.
21. Reflexive Property of
22.
23.
H
|
; SSS
|
J
F
G
24. If a figure is not a rectangle¸ then all of its angles are not right angles.
25. 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.