Download Geometry Midterm Exam Review

Geometry Midterm Exam Review
Complete each statement with the word always, sometimes, or never.
1) Collinear points are ______ on one line.
2) Two noncoplanar lines _______ intersect.
3) A bisector of a segment ________ intersects the segment at its midpoint.
4) If two angles are complementary, then they are ________ adjacent angles.
5) If a triangle is isosceles, then it is _______ a right triangle.
6) Vertical angles are _______ congruent.
7) If an angle is acute, then its supplement is __________ acute.
8) If a polygon is equilateral, then it is ________ a regular polygon.
9) Three planes ________ intersect in a line.
10) If two lines are parallel, then they are _________ coplanar.
11) If two planes intersect then they are ________ parallel.
12) A scalene triangle _______ has an acute angle.
13) If all three angles in one triangle are congruent to all three angles in another triangle
then the triangles are __________ congruent.
14) Consecutive angles of a rhombus are ____________ complements.
15) Two noncoplanar lines are ___________ skew lines.
16) Diagonals of a parallelogram are _____________ perpendicular.
17) Two obtuse angles are __________ complementary.
18) If a conditional statement is true, then the contrapositive of the inverse is _____true.
19) If one angle in an isosceles triangle is 60°, then the triangle is _________equilateral.
20) Opposite angles in a square are ________ congruent.
Complete the following.
21) The coordinates of L and X are -12 and10, respectively. N is the midpoint of segment
LX, and Y is the midpoint of segment LN. Sketch the diagram then answer the following.
a) LN =
b) coordinate of N
c) LY =
d) coordinate of Y
22) Find the measure of an angle that is four times as large as its supplement.
23) If < 1 and < 2 are supplementary, what type of angle is < 1?
m< 1 = 7x - 10
m< 2 = 3x -20
In the diagram, OT  YS. Use the diagram and this information to solve for all variables.
24) m< 1 = x2
m< 4 = 100 – 21x
V
Y
25) m< 3 = 7x - 10
m< 4 = 2x + 10
4
3
O
2
1
26) m< 1 = 4x + 12
27) m< 1 = 3x - 15
m< VOS = x + 13
R
T
S
m< 3 = 2x – 10
28) m< VOT = 7x – y + 9
m< 1 = 50
and m< YOR = 5x + 2y + 11
29) The lengths of the sides of a triangle are 2x + 5, 3x + 10, and x + 12. Find all the
values of x that make the triangle isosceles.
30) The sum of the measures of the exterior angles of any polygon equals ?
31) The sum of the interior angles of a decagon equals?
Solve for all unknown variables.
32)
33) Given that WX = x + 2 , XY = x + 2,
RS = 4x – 10, and ST = 3x + 8
25°
32°
R
W
S
2x°
X
T
34) If HI = 4x, LM = 2x + 3, and
KJ = x – 2, then x = ______
Y
35) Given that TDKR is a parallelogram.
T
2x + y
D
J
K
4x - y
L
H
24
M
H
I
36)
R
36
K
37)
(90 – x)°
2x°
54 – 3x
x2 – 2x
x2
38)
39) Given that m< EFI = m< IFG and
m< EGI = m< IGF
E
x°
80°
5x
120°
I
x°
F
40)
G
41)
(x + 2y)°
x
(2x + y)°
20°
125°
42)
43) ABCDE is regular
A
x
(2x + 9)°
E
y B
65°
(3x -2)°
z
C
D
44)
45) given that the pentagon is regular
x°
135°
(x – 2)°
2x°
(x + 5)°
110°
x°
46) the given quadrilateral is a
parallelogram
47)
125°
y°
x°
120°
x°
___
48) GM is the median of ∆IRG
I
M
x°
132°
G
R
49) A supplement of an angle is six times as large as a complement of the angle. Find the
measures of the angle, its supplement, and it complement.
50) Given that the triangle is equilateral and M and N are midpoints of the sides, find the
perimeter of the triangle.
M
12
N
51) The lengths of two sides of a triangle are given. Write the numbers that best complete
the statement: The length of the third side must be greater than ____ but less than ____.
Given sides: 6, 9
52) In ∆XYZ, if m< X = 32° and m< Z = 75°, what is the longest side of the triangle?
53) solve for x, y, and z
z°
x°
x°
120°
y°
54) List all the postulates and theorems (ex. ASA) that can be used to prove triangles
congruent.
55) What does CPCTC stand for? Does it come from a postulate, theorem, corollary, or
definition?
56) If points R and S are on a number line at 2 and 8 respectively, how many different
points can be drawn above or below the number line that would be the same distance
from both R and S?