Name:
Date:
Geometry Midterm Review
Calculate the missing measure. Find the value of the given variables.
1) Suppose R, S, and T are three points on a line. What relation involving RS, ST, and RT must
be true if R is between S and T?
2) If m<ABC =180 and point G is in the interior of <ABC and a ray is drawn from a point on <ABC
through point G, what can you deduce about the two angles?
3) G, H, K are three points on a line. Which of the following statements can be true?
a) K is between G and H, and H is between G and K.
b) H is between K and G, and H is between G and K.
c) G is between H and K, and K is between G and H.
d) K is between H and G, and G is between K and H.
e) G is between K and H, and G is between H and K.
4) A, B, and C are three points on a line. The coordinates of A and B are -2 and 8, respectively. If
C bisects AB, what is the coordinate of C?
5) A, B, and C are three points on a line. The coordinate of A is 0 and the coordinate of C is -6. If
B is the midpoint of AC, what is the coordinate of B?
6) Using the figure, determine the following.
a) m<SPR + m<QPO = m< ______
b) m<RSQ + m<_______=m<RSP
c) m<POQ + m<POS = ________
d) m<SRQ – m<SRO = m<________
e) M<ROQ = 180 – m< ________
f) SO + OQ = _______
7) Ray AB and Ray AC form a right angle. How are the two rays related to one another?
8) If the sum of the measures of two angles is 90, then the angles are called
_________________. The angles individually are classified as _________ angles.
9) The supplement of an acute angle is a/an____________ angle.
10)The complement of an acute angle is a/an ____________ angle.
11) If the measure of an angle is twice the measure of its complement, what is the measure of
each angle?
Calculate the missing measure. Find the value of the given variables.
10
6
13)
12)
x
x+2
12
18
2x +1
15)
14)
70o
2x+8
55o
yo
3x+12
xo
16) The diagonals of a trapezoid _____bisect each other?
a) Always
b) Sometimes
c) Never
17) If corresponding angles of two polygons are congruent, then the polygons are
_____ similar.
a) Always
b) Sometimes
c) Never
18) If the lengths of the base of a trapezoid are 19 and 33, then the length of the
median is _____.
a) 52
b) 14
c) 26
d) 21
e) None of these
19) If the length of two sides of a triangle are 7 and 13, then the length of the third side
must be between ____ and ____.
a) 8,12
b) 7,19
c) 7,20
d) 6,20
e) None of these
20) If triangle QRS, QR = 6, RS = 7, and QS = 8. The largest angle of the triangle is
_____.
a) <Q
b) <R
c) <S
d) None of these
21) The ratio of the measures of two complementary angles is 4:11. The measure of
the larger angle is _____.
a) 48
b) 66
c) 24
d) 132
e) None of these
Rewrite the following conditional statements as an inverse, converse, and contrapositive.
22) If the dog walks himself, then you are a good trainer.
Inverse: __________________________________________________________________
Converse: ________________________________________________________________
Contrapositive: ____________________________________________________________
23) The faucet works only if you turn it on.
Inverse: __________________________________________________________________
Converse: ________________________________________________________________
Contrapositive: ____________________________________________________________
Determine if the statement is >, < or =.
24) If x > y and y = z, then x ____ z.
25) If a > b, and c < b, then c ____ a.
26) If s = t + 4, then s ____ t.
27) If e + 5 = f + 4, then e ____ f.
28) GIVEN: MK  OK; KJ bisects <MKO.
M
PROVE: JK bisects <MJO
J
1
2
3
4
O
Statements
Reasons
1)
_____________________
1)
Given
_______
2)
____________________
2)
Given
_______
3)
<3  <4
3)
4)
_____________________
4)
5)
MJK  OJK
5)
_______
6)
<1  <2
6)
___________________________________
7)
JK bisects <MJO
7)
_______
_______
Reflexive Property
_______
K
Decide whether you can use SSS, SAS, ASA, AAS, or HL to prove the triangles congruent.
If so, identify the postulate/theorem. If not, write “not possible”.
29)
30)
S
U
N
M
W
Postulate/Theorem: ___________________
or Not Possible
T
U
S
A
C H
32)
V
D
D
C
Postulate/Theorem: ___________________
or Not Possible
G
E F
Postulate/Theorem: __________________
or Not Possible
34)
B
Q
Postulate/Theorem: __________________
or Not Possible
Postulate/Theorem: ___________________
or Not Possible
33)
S
V
T
31)
PR
Q
R
T
S
Postulate/Theorem: __________________
or Not Possible
35) Find the value of x and y in order for each figure to be a parallelogram.
(4x+2y)°
(4y+x)°
(a)
(b)
80°
7y
(c)
(3x)°
(45)°
Classify each statement as always, sometimes or never.
_____________________ 36) A square is ____ a rectangle.
_____________________ 37) A rhombus is ____ a square.
_____________________ 38) A trapezoid ____ has three congruent sides.
_____________________ 39) A rectangle is ____ a rhombus.
_____________________ 40) A rhombus is ____ a parallelogram.
_____________________ 41) The diagonals of a trapezoid ____ bisect each other.
_____________________ 42) The diagonals of a rectangle ____ bisect each other.
_____________________ 43) The diagonals of a parallelogram ____ bisect each other.
Complete the table for regular polygons.
44)
45)
46)
12
6
10
Number of Sides
47)
Measure of each
exterior angle
48)
8
Measure of each
interior angle
168
Complete each statement by writing <, =, or >. Given m<2 > m<1 + m<5
49)
m<1 __________ m<4
2
50)
m<2 __________ m<1
5
51)
m<3 __________ m<2
52)
m<4 __________ m<2 + m<1
1
3
4
53) The sum of the measures of the interior angles of a polygon is five times the sum of the
measures of its exterior angles. How many sides does the polygon have?
54) Determine the measure of the complement of an angle whose measure is
a) 20
b) 68
c) 46.5
d) n
e) 45 + n
55) What is the measure of an angle, given that the measure of its supplement is 39 more than
twice the measure of its complement?
56) If two lines intersect, how many pairs of vertical angles are formed?
57) Identify the hypothesis and conclusion for each of the following statements. Write its
converse, contrapositive, and inverse. If both the conditional statement and the converse are
TRUE, write a biconditional statement. If they are NOT TRUE, give a counterexample.
a) If two angles are complementary, then each of them is acute.
b) If a = b and b = c, then a = c.
c) If a = b, then a + c = b + c.
d) If the dimensions of a rectangle are a and b, then its area is ab.
e) If two planes intersect, then their intersection is a line.
The lengths of two sides of a triangle are given. Write the numbers that best complete each
statement.
58)
9, 11
The third side has to be less than ___________ but greater than
___________.
59) 2x, 16y, where x>y
The third side has to be less than ___________ but greater than
___________.
60)
The third side has to be less than ___________ but greater than
_____________.
10, 10
61) Given the indicated lines are parallel, determine the value of x.
a)
b)
c)
d)
e)
f)
AB || CD and EF bisects <AFG.
1) If m<1 = 100, find the measure of the numbered angles.
2) If m<3 = 4x -9 and m<5 = x + 19, find the measure of each of the numbered angles.
62) Find the value of x given each diagram.
a)
b)
c)
Find the value of x.
63)
64)
40°
40°
5x - 8
x°
2x + 7
126°
(90-x)°
65)
66)
2x°
140°
3x°
67) Given: w ll z; k ll l. Find the values of the variables.
z
w
n
h
k
70
d
e
j
f
l
g
m
k
c
b
a
l
52
Justify each statement with a property from algebra.
68) If 6x-7 = 29, then 6x = 36. _____________________
69) If RS = TW, then TW = RS.
_______
70) 2 (a + b) = 2a +2b. __________________________
71) If AB = CD, CD = EF, and EF = 23, then AB = 23. ___________________
72) If 5y = -20, then y = -4 _________________
73) 3(x+y) = 3x + 3y ____________________
74) If 2(x+1) = 8, then 8 = 2(x+1). _____________________
Complete each statement with the word “always”, “sometimes”, or “never”.
75) Two skew lines are _________________ parallel.
76) Two parallel lines are ______________ coplanar.
77) A line in the plane of the ceiling and a line in the plane of the floor are ________________
parallel.
78) Two lines in the plane of the floor are _______________ skew.
79) A line in the plane of a wall and a line in the plane of the floor are
(a) _____________ parallel
(b) _____________ intersecting
(c) _____________ skew
Find the values of x and y. Show ALL work! Circle your answer! **Diagrams not drawn to
scale!**
80)
81)
(x - y)°
70°
(4x – 2y)°
(4x + 2y)°
(2x - y)°
90°
50°
30°
82) QUADRILATERALS
Four-sided figures
parallelogram
trapezoid
Isosceles
trapezoid
rectangle
rhombus
square
kite