Download Geometry Midterm Review Name

Geometry Midterm Review
Name: _________________________
1.) Refer to the figure to the right.
a.) Name three points that are collinear.
b.) Where does FG intersect plane B?
c.) Which four points in the figure are coplanar?
2.) The sum of the measures of two supplementary angles is always _________.
3.) What is the supplement of a 45 degree angle? ___________
4.) The sum of the measures of two complementary angles is always _________.
5.) Find the value of x so that AFC is a right angle.
Show all work!
Determine the slope of the line that contains the given points.
6.) A(0, 2) and B(7, 3)
7.) W(3, 2) and X(4, -3)
Determine whether PQ and UV are parallel, perpendicular, or neither.
8.) P(-3, -2), Q(9, 1), U(3, 6), V(5, -2)
9.) P(5, -4), Q(10, 0), U(9, -8), V(5, -13)
10. ) What is the midpoint of the segment having endpoints X (-2, 8) and Y (7, 4)?
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Refer to the figure to the right, and circle the correct answer for questions 11-14.
11.) Which pair of angles are complementary?
a.) USV , VSW
b.) VSW , WSR
c.) TSV , VSR
d.) TSR, USW
12.) Which angle is vertical to UST ?
a.) VSW
b.) USV
c.) TSR
d.) WSR
13.) Which angle creates a linear pair with USW ?
a.) UST
b.) USV
c.) TSR
d.) VST
14.) Which angle is adjacent to WSV ?
a.) RSV
b.) UST
c.) TSR
d.) USV
15.) Which statement is true given that K is between J and L?
a.
b.
c.
d.
JK + KL = JL
JL + LK = JK
LJ + JK = LK
JK  KL
16.) Name each polygon by its number of sides. Then classify it as convex or concave and regular or irregular.
a.)
b.)
_______________
c.)
_________________
________________
_______________
_________________
________________
_______________
_________________
________________
17.) The measures of two complementary angles are in the ratio 7:8. What is the measure of the larger angle?
a. 42
b. 48
c. 84
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d. 96
18.) Find the measure of each numbered angle.
a.) m1  5x  20
b.) m1  8 x  18 and m2  16 x  6 .
m2  3x  80
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2
c.)
7 and 9 are complementary.
m7  6x 15 and m9  2x  21
For Problem 19-20 Write the converse, inverse, and contrapositive of the conditional statement.
19.)Conditional: If the month is March, then it has 31 days.
Converse:
Inverse:
Contrapositive:
20.)Conditional: If the angle is obtuse then it is more than 90 degrees.
Converse:
Inverse:
Contrapositive:
21.) If AB  BC , AB = 4x – 2 and BC = 3x + 3, find x
a. 5
b. 4
c. 3
3
d. 2
22.) If BD bisects ABC , mABD = 2x + 3 and mDBC = 3x – 13, find mABD .
23.) Determine whether each statement is always, sometimes, or never true. Justify your answer.
a.) Two segments that have the same measure are congruent.
b.) The intersection of two lines is a plane.
c.) Two angles whose sum is 180 form a linear pair.
d.) A plane contains at least three points not on the same line.
24.) Which is a valid conclusion for the statement:
 R and S are vertical angles?
a. mR  mS  180
b. mR  mS  90
c. R and S are adjacent
d. R  S
25.) If P is in the interior of MON and mMOP  1 / 2 mMON , what can you conclude?
a. PON  NOM
b. MON is an acute angle
c. OP is the angle bisector of MON
d. mMON  mPON
Prove the following by writing a two-column proof.
26.)
Given: 2x  7  4
Prove: x 
Statements
11
2
4
Reasons
27.) Given: 6 x  2( x  1)  30
Statements
Prove: x  4
28.)
Identify each pair of angles from the following descriptions.
a.) Name all pairs of vertical angles.
b.) Name each linear pair.
c.) Name all pairs of alternate interior angles.
d.) Name all pairs of alternate exterior angles.
e.) Name all pairs of consecutive interior angles.
f.) Name all pairs of corresponding angles.
29.) Find the value of y.
30.) Find the values of w and z.
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Reasons
31.) Find h so that the lines are parallel.
32.) What parts of an equiangular triangle are equal?
33.) If corresponding parts of triangles are congruent, what relationship do the triangles have?
34.) The 3 angles of any triangle sum to what number?
35.) What is the measure of each angle in an equiangular triangle?
36.) What are the equal sides of an isosceles triangle called?
37.) What is the exterior angle theorem?
38.) What are 3 ways to classify triangles by angles?
39.) What is an included angle?
40.)
From
triangle.
the
information
given,
determine
∆CAB  ∆ _______________
the
correct
congruent
∆XGH  ∆ _______________
41.) Name the congruent angles and sides for each pair of congruent triangles.
a.) ∆TUV  ∆XYZ
b.) ∆CDG  ∆RSW
Angles:
Angles:
Sides:
Sides:
42.) Find the value of GE if E is between G and O in the given figure:
G

2x E

6x + 8
O

36
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name
of
the
other
43.) Given m3  67 , find the following angle measures.
a.) 1 __________
b.) 2 __________
c.) 3 __________
d.) 4 __________
e.) 5 __________
f.) 6 __________
g.) 7 __________
h.) 8 __________
44.) Given m7  107 and m10  86 , find the following angle measures.
a.) 1 __________
b.) 2 __________
c.) 3 __________
d.) 4 __________
e.) 5 __________
f.) 6 __________
g.) 7 __________
h.) 8 __________
i.) 9 __________
j.) 10 __________
k.) 11 __________
l.) 12 __________
m.) 13 __________
n.) 14 __________
o.) 15 __________
p.) 16 __________
45.) Decide whether you can use the SSS, SAS, ASA Postulate or the AAS Theorem to prove the triangles congruent. If
so, write the congruence statement, and identify the postulate or theorem. If not, write not possible.
a.)
b.)
c.)
d.)
e.)
f.)
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46.) Find m1 in the following figure.
47.) Find the value of x.
48.) Find g so that the lines are parallel.
49.) Write the correct triangle congruence statement for each pair of marked triangles.
T
a.
Y
W
Q
R
M
b.
X
E
C
50.) . Using the congruence statement QRS  FGH , find mG
H
S
400
Q
300
R
N
G
F
8
D
51.) In the figure, QP and QR are opposite rays, and QT bisects RQS .
If mRQT  6 x  5 and mSQT  7 x  2 , find mRQT .
Show all work!
52.) Find the perimeter of a regular pentagon whose sides measure 4 meters. Show all work!
53.) Find the length of one side of a regular triangle if the perimeter is 12 inches. Show all work!
54.) A rectangular basketball court has a perimeter of 232 feet. The length of the court is 32 feet greater than
the width. What is the width of the basketball court?
a.) 42 feet
b.) 74 feet
c.) 84 feet
d.) 100 ft
55.) Find the value of x and AP, if P is between A and B and AB = 42 cm, AP = 6x – 4, and PB = 10 cm.
56.) If 2 = 75, what is the measure of its supplement?
57.) Find SR if R is the midpoint of SU
2(5a – 4)
6a + 4
S
R
U
58.) Is (-2, 5) a solution of 3x + 4y = 14?
Write an equation in both point-slope form and slope-intercept form for the line that satisfies the
given conditions.
59.) slope = -3, contains (-2, 6)
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60.) What is the perimeter of triangle DEF if its vertices are D (-2, -6), E (-2, 6), and F (3, -6)?
Write an equation in slope-intercept form for each line.
61.) l
62.) parallel to l, contains (-1, 6)
63.) perpendicular to l, contains (4, -5)
64.) A graph of a linear equation is shown below.
Which equation describes the graph?
a.
b.
c.
d.
y = 0.5x – 1.5
y = 0.5x + 3
y = 2x – 1.5
y = 2x + 3
65.) Line p contains the points (9, 7) and (13, 5). Which equation represents a line perpendicular to line p?
a. –2x + y = –11
b. –x – 2y = –2
c. –x + 2y = 5
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d. 2x + y = 31
66.) In the diagram below, B is a point on AC such that  ADB is an equilateral triangle, and
isosceles triangle with DB  BC . Find m∠C.
 DBC is an
67.) On a city map, WHHS is located at position (5. -4) and the mall is located at (10, 6).
What is the slope of the line between WHHS and the mall? ________
What is the distance between WHHS and the mall according to this map? _________
If you were meeting a friend halfway between WHHS and the mall, what would be the coordinate of
the location where you will meet? _________
Graph the location of WHHS and the mall on the coordinate plane below. Show the meeting place on
the map as point M, show WHHS as point W, and the mall as point S.
(some formulas you may need:
d
x2  x1 2  y2  y1 2
m
y 2  y1
x2  x1
 x  x y  y2 
M  1 2 , 1

2 
 2
What is the distance between WHHS (W) and your meeting place (M)? __________
If you lived perpendicular to the line made between W and S from M (the meeting place), what
would be the equation of the line to your house? ________________________
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68.) In the diagram below, m∠A = x, m∠B = 2x + 15 and m∠ACD = 5x + 5. What is m∠B?
69.) Find the slope of a line perpendicular to the line whose equation is 2y – 6x = 4.
R
S
Complete the 2 column proof:
70.) Given : CS  AC
BC  CR
C
Prove: RSC  BAC
A
_____________Statements
1.
CS  AC
BC  CR
B
Reasons__________________
1. Given
N
O
71.) Given : LM  NM
O is the midpoint of LN
L
Prove: NMO  LMO
M
Reasons__________________
_____________Statements
1.
LM  NM
O is the midpoint of LN
1. Given
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