Download Midterm Exam

Name __________________________________________ Period _____ Date ________
GEOMETRY
FALL SEMESTER REVIEW
1) Draw and label BH intersecting plane S.
2) X is between Y and Z.. YZ  28 , and XZ  22.8 . Find YX.
3) BD bisects ABC , m ABD   4 x  5  , and m DBC   3x 1  . What is
the value of x?
A
D
B
C
4) Given: m 1  (3x  5) and m 4  (7 x  5)
a) Find the measures of 1, 2, 3, and 4.
b) What do you notice about the m 2 and m 4 ?
1
4
2
3
5) Given AD  CD , find the area of ABC .
C
5
A
3
3
B
1
D
6) Write the following statement as a biconditional:
“If it has two wheels, then it is a bicycle.”
7) Write the following statement as a biconditional:
“A cube is a 3 dimensional solid with 6 square faces.”
8) Given: HI  2 x  6, IJ  3x  3, and HJ  7 x  3 . Write a justification for each step in
the following proof:
H
HJ = HI + IJ
____________________________
7 x  3   2 x  6   3x  3
____________________________
7 x  3  5x  3
____________________________
7 x  5x  6
____________________________
2x  6
____________________________
x3
____________________________
I
J
9) Which graph best represents a line that is parallel to 4 x  5 y  10 ?
(A)
(B)
(C)
(D)
10) Given that
4  11 , which lines are parallel and why?
l
m
1
2
5
3
6
9
4
7
r
8
10
11
12
t
(A) Lines l and m are parallel, because alternate exterior angles are congruent.
(B) Lines l and m are parallel, because corresponding angles are congruent.
(C) Lines r and t are parallel, because corresponding angles are congruent.
(D) Lines r and t are parallel, because alternate exterior angles are congruent.
(E) This is not enough information to prove that two lines are parallel.
In #11-12, use the point K(7, 4) and H(-1, 8) to answer the given problem.
Let the midpoint of KH be L.
11) What are the coordinates of L?
(Use the midpoint formula.)
12) Find the length of KH .
(Use the distance formula.)
13) If you were to extend the ends of KH so that you create a line, what is the slope of
line KH?
14) Write a linear equation that represents a vertical line. Then, graph your line on the
coordinate plane.
y
Equation:_______________
5
x
-5
-5
5
15) The location of three food stands on a fair’s midway are shown. What is the measure
of the angle labeled xo?
x◦
146◦
155◦
16) Complete the Proof:
Q
Given:
N
R
P
R
P is the midpoint of QR
Q
S
Prove: NPQ  SPR
Statements
1. Q  R
2. P is the midpoint of QR
3. QP  RP
4. NPQ  SPR
5. NPQ  SPR
Reasons
1.
2.
3.
A.
B.
C.
D.
E.
Given
ASA Postulate
Given
Definition of a Midpoint
Definition of Vertical Angels
4.
5.
17) P is the midpoint of TS and TR  SR  1.4in . What can you conclude about
TRP & SRP ?
R
A. TRP  SRP by SAS
B. TRP  SRP by SSS
C. TRP  SPR by SAS
D. TRP  SPR by SSS
T
Find the following measurements (make sure calc. is in degree mode)
18.) cos (45)
19.) sin (52)
20.) tan -1 (.77)
P
S
21) A Yield sign is an equiangular triangle. What are the lengths of the sides?
 n  6 in
YIELD
3n 10 in
22) HJ has endpoints H  5,3 and J  4, 3 .
What is the y-intercept of the line that is the
perpendicular bisector of HJ ?
Show your answer as an ordered pair.
y
5
x
-5
-5
23) The diagram shows the coordinates of the
vertices of a triangular patio umbrella. The
umbrella will rest on a pole that will support it.
Where should the pole be attached so that the
umbrella is balanced?
A)  5,4
 14 
C)  4, 
 3
B)  4,5
 14 
D)  , 4 
 3 
5
24) A triangle has coordinates A  0,6  , B 8,6  ,
y
10
and C  5,0  . CD is a median of the triangle and
A
CE is an altitude of the triangle.
B
Which of the following is true?
A. coordinates of D and E are the same
B. distance between D and E is 1 unit
C. distance between D and E is 2 units
D. D is on the triangle and E is outside the
triangle
-10
-10
10
25) Find each of the following measures using the diagram. Note: HI and HG are
midsegments, ED  18.2, HG  17.5 , and m GHI  58 .
A. HI
E
B. GE
C. m HGD
G
H
D
F
I
26) Write an inequality comparing AB to DE.
E
C
12
B
85
10
12
95
A
D
10
F
x
C