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Honors Geometry Midterm 2013/2014
Name:_________________________Date:______________Hour:_________
1. Rewrite the statement in if-then form: Every isosceles triangle has two congruent sides.
[A] A figure has two congruent sides if and only if it is an isosceles triangle.
[B] A figure is an isosceles triangle if and only if it has two congruent sides.
[C] If a figure has two congruent sides, then it is an isosceles triangle.
[D] If a figure is an isosceles triangle, then it has two congruent sides.
2. Find the converse of “If it is Friday, then I go for a drive.”
[A] If it is not Friday, then I do not go for a drive.
[B] If it is Friday, then I do not go for a drive.
[C] If I do not go for a drive, then it is not Friday.
[D] If I go for a drive, then it is Friday.
3. Identify the inverse of the statement A square has four sides.
[A] If a figure is a square, then it has four sides.
[B] If a figure does not have four sides, then it is not a square.
[C] If a figure has four sides, then it is a square.
[D] If a figure is not a square, then it does not have four sides.
4. Identify the contrapositive of the statement Two congruent angles have the same measure.
[A] If two angles do not have the same measure, then they are not congruent.
[B] If two angles are not congruent, then they do not have the same measure.
[C] If two angles have the same measure, then they are congruent.
[D] If two angles are congruent, then they have the same measure.
5. Which of the following is a valid conclusion that can be reached from statements (1) and (2)?
(1) If two angles form a linear pair, then they are adjacent.
(2) If two angles are adjacent, then they share no common interior points.
[A] If two angles are adjacent, then they form a linear pair.
[B] If two angles form a linear pair, then they share no common interior points.
[C] If two angles share no common interior points, then they form a linear pair.
[D] If two angles form a linear pair, then they are congruent.
b
g
b g
6. Find the distance between the points P – 5, – 1 and Q 4, – 2 .
[A]  10
[B]
[C]
82
10
[D] 82
7. Find the midpoint of CD.
y
10
D
–10
10 x
C
–10
b g
b g
[A] – 1, 2
[B] 2, – 1
b g
[C] – 2, 1
b g
[D] 1, – 2
8. In the figure, BA and BC are opposite rays, BF bisects ABE, and BD bisects EBC.
F
E
D
A
B
C
If mABF  8 x  15 and mFBE  10 x  1, find mABF .
[A] 68°
[B] 75°
[C] 71°
[D] 61°
9. In the figure, QT bisects UQR and QS bisects RQT.
R
Q
S
T
U
If mUQT  12a  9 and mTQR  18a  9, find a.
10. Name the polygon by its number of sides and then classify it as irregular or regular and convex
or concave.
Find the value of the variable and BC, if B is between A and C for #11 & 12.
11. AB  30, BC  3x, AC  48
[A] 5; 15
[B] 7; 21
[C] 6; 18
[D] 8; 24
12. AB  3y  1, BC  2 y, AC  36
13. Find BC.
A
1
9
cm
16
2
B
C
1
cm
4
14. Given: AC || DF and m ABH  147. Find mDEG .
15. Find the value of x, y, and z in the figure.
38°
b2xg
b2 y  6g
b8z  6g
16. Which shows the completed truth table?
[A]
p
T
T
F
F
q
T
F
T
F
pq
T
T
F
T
pq
F
T
F
F
[B]
p
T
T
F
F
q
T
F
T
F
pq
T
F
F
F
pq
T
T
T
F
[C]
p
T
T
F
F
q
T
F
T
F
pq
F
T
T
T
pq
F
F
F
T
[D]
p
T
T
F
F
q
T
F
T
F
pq
F
T
F
F
pq
T
T
F
T
17. If RG is the angle bisector of TRI and mTRI  5x  9 and mIRG  3x  10, find x and
mTRI .
R
T
G
I
[A] x  8 ; mTRI  31
[C] x  15 ; mTRI  66
[B] x  6 ; mTRI  21
[D] x  11 ; mTRI  46
18. In KHD, mKHS  10 y  5, mSHD  11y  1, and mKHD  130. Find y and mSHK if
HS is the angle bisector of DHK.
H
L
D
S
K
19. Find the value of x and the m2 if QR is an altitude of QST , m1  4 x  6 , and
m2  5x  3 .
Q
U
T
2 1
R
S
[A] x  11, m2  38
[C] x  2, m2  11
[B] x  2, m2  79
[D] x  11, m2  52
20. Determine the relationship between the lengths of the given sides.
GS , ES
21. The measures of two sides of a triangle are 9 and 10. Use an inequality to express the range of
the measure of the third side, m.
22. Two sides of a triangle have sides 5 and 12. The length of the third side must be greater than
_____ and less than ____.
[A] 6, 18
[B] 7, 17
[C] 5, 12
[D] 4, 1323.
23. Write an inequality relating the given segment measures.
AB, CD
D
16
27°
A
30°
C
B
16
[A] AB  CD
[B] AB  CD
[C] AB  CD
[D] none of these
24. Which postulate can be used to prove that FBD  CBD if FB  CB and FD  CD ?
[A] SSS
[B] SAS
[C] ASA
[D] These triangles cannot be proven congruent.
25. Which parts must be congruent to prove that HJK  HJI by the SSS postulate?
[A] HK  HI
[C] HK  HI and KJ  IJ
[B] KJ  IJ
[D] HI  JI and HK  JK
26. Which postulate can be used to prove that XVY  ZVW if V is the midpoint of XZ and
YW ?
[A] SAS
[B] ASA
[C] SSS
[D] The triangles cannot be proven congruent.
27. Which postulate can be used to prove that KHJ  IHJ ?
[A] SAS
[B] SSS
[C] ASA
[D] The triangles cannot be proven congruent.
28. Determine whether the pair of triangles below are similar. If similarity exists, write a
mathematical sentence relating the two triangles. Give a reason for your answer.
Y
Q
11.7
7.2
6
10
P
X
4
R
6
Z
29. Classify the triangle with angles measuring 52, 38, and 90.
[A] obtuse
[B] right
[C] acute
[D] none of these
30. What is the measure of angle x?
x
31°
[A] 27
[B] 149
[C] 29
[D] 59
31. Find the value of x.
86°
x
123°
32. List the six pairs of congruent corresponding parts if PQR  TSR.
Q
S
P
R
T
33. Which postulate or theorem can be used to show that the triangles are similar?
M
30°
B
115°
115°
A
35°
[A] SSS Similarity
C] AA Similarity
N
C
P
[B] SAS Similarity [
[D] The triangles are not similar.
Cumulative Review for Mid Term – Geometry Part 1 – Answers.
[1] [D]
[2] [D]
[3] [D]
[4] [A]
[5] [B]
[6] [B]
[7] [D]
[8] [C]
[9] 3
[10] pentagon; regular; convex
[11] [C]
[12] 7; 14
[13]
11
cm
16
[14] 33
[15] x  26, y  16, z  17
[16] [B]
[17] [D]
[18] y  6; mSHK  65
[19] [D]
[20] GS  ES
[21] 1 < m < 19
[22] [B]
[23] [A]
[24] [A]
[25] [C]
[26] [A]
[27] [C]
[28] No; sides are not proportional.
[29] [B]
[30] [D]
[31] 151°
[32]  P  T , Q   S ,  PRQ  TRS , PQ  TS , PR  TR , QR  SR
[33] [C]