Geometry
Name
_________________________________________
MIDTERM EXAM REVIEW – UNIT 1 BASICS
OF
Period __________
GEOMETRY
Important Note: This study guide is a just a sample of the concepts and
applications covered in the unit. You are responsible for all of the material covered
in class notes, homework, activities, reviews, quizzes, and test. Be sure to review
all resources that are available to you including the online vocabulary and reviews
from your textbook.
I.
1)
2)
Using the figures shown, identify the indicated quantities.
Using the figure at the right, complete the following.
a)
Name a line that is contained on plane N. __________
b)
Are P, Q, R, and S are coplanar? Explain.
c)
Are P, R and T coplanar? Explain.
M
e
d
•P
d)
Name the intersection of line d and plane N. __________
e)
Name the intersection of plane M and plane N. __________
•R
•S
N
•Q
•T
Use the figure at the right to determine whether each statement is True or False.
a)
Point C lies on line l.
b)
Point E lies on AB .
c)
Points D, A, and B are collinear.
d)
Points D, A, and B are coplanar.
e)
Point C lies on line m.
KD/MPH/KAL/CR 12/14
f)
Lines l and m intersect at E.
1
Geometry
II.
Sketch and label the following diagrams.
1)
K intersects line AB and C.
2)
1 and 2 are vertical angles.
3)
3 and 4 are adjacent angles
4)
Segment TR is bisected by segment
SA at Y.
III.
For each of the following find the indicated quantities.
1)
G, U, and M are collinear. If MG = 29 and UM = 14, find UG.
2)
Point A is between points C and T. Find AT if CA = 10 and CT = 23.
3)
Q is between P and S. R is between Q and S. S is between Q and T.
If PT = 30, QS = 16, and PQ = QR = RS, find PQ, ST, and RP.
4)
Segment MD is bisected by line l at I. If MI = 4x – 8 and ID = 8x – 32, find x
and MD.
KD/MPH/KAL/CR 12/14
2
Geometry
IV.
1)
Complete each of the following questions using the appropriate formula(s).
Use the distance formula to determine if PQ @ QR given P (-4, 3), Q (-2, 1), and
R (0, -1).
2)
Using points P, Q, & R from #1, find the midpoints of PQ, QR, and PR .
3)
Given that segment PQ has one endpoint at P (–5, 1) and its midpoint at M (1, –1),
find the coordinates of the other endpoint, Q. Show all work.
V.
1)
Using the figure shown, identify each of the following.
Give another name for
E
.
B
2)
C
Name a pair of opposite rays.
3
F
1
G
D2
A
3)
Name the vertex of 3.
4)
Give another name for 1.
5)
Name the sides of 2.
6)
Name a linear pair.
7)
Name a pair of complementary angles.
KD/MPH/KAL/CR 12/14
3
Geometry
VI.
For each of the following find the indicated quantities.
1)
Ray QS is the bisector of PQR. Find the measure of SQR
and PQR.
2)
If the m3 = 50 find the measure of angles 1, 2,
and 4.
3)
Ray BD bisects ABC. Find the value of x.
4)
Find the value of x and y.
5)
A and B are complementary. Find mA and mB if mA = (7x + 1) and
mB = (5x – 7).
6)
The sum of an angle and three times its complement is equal 38 more than its
supplement.
KD/MPH/KAL/CR 12/14
4
Geometry
VII.
1)
Use the diagram at the right to complete Questions 1 – 4.
J
If
bisects KMQ, mEMQ = (3x + 2), and
mKME = (4x – 15), find x and mKMQ.
A

E

M
F
Q
2)
If mFMA = (3x + 7) and mKME = 5x – 8, find x.
3)
If mKME = (2x + 8) and mKMJ = (x – 2), find x.
4)
If mKMQ = (x2 + 156) and mFMQ = (2x2 – 14x), find x and mFMQ.
KD/MPH/KAL/CR 12/14
K
5
Geometry
VIII. Use the diagrams to complete the following questions.
1)
2)
IX.
Using the diagram at the right, complete the following
questions.
a)
Name the circle. ___________
b)
Name two radii. ___________________
c)
Name a diameter. ___________
d)
Name two chords. ___________________
e)
Name a line that would represent a secant. ___________
f)
Name a line that would represent a tangent. ___________
In the figure at the right, circle F has a diameter of 5
cm, and circle G has a diameter of 6 cm. Find the
indicated measures.
a)
AB ___________
b)
BF ___________
c)
FG ___________
d)
AG ___________
e)
BC ___________
f)
FC ___________
h)
AC ___________
Given the equation (x + 3)2 + (y – 2)2 = 20, identify:
1)
the center ___________
3)
whether the following points lie inside, outside, or on the circle
(-3, 6)
KD/MPH/KAL/CR 12/14
2)
the radius ___________
(1, 4)
(1, -6)
6
Geometry
X.
Write the equation of each circle described.
1)
The center is (-3, 0) and the diameter is 22 units.
2)
The center is (4, -11) and passes through (12, -9).
3)
The circle has a diameter with endpoints of (-3, 10) and (7, 14).
XI.
Express the following circle in standard form then identify the center,
radius, circumference and area.
x2 + y2 - 4x + 8y – 12 = 0
Standard Form ___________________________
Center ____________
Radius ____________
Circumference _______________
Area _______________
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