2nd Semester Midterm Review
NAME: ____________________________________p. ______
Chapters 6, 8, 9, 10
CHAPTER 6
19.
The diagonal of a square is 22cm. Find the
perimeter of the square.
20.
MINT is a rectangle. MS
IS 2x 35 . Find MN.
Determine if the statement is…
(S)ometimes, (A)lways, (N)ever true
1.
A square is a rhombus.
2.
A rectangle is a rhombus.
3.
A rhombus is parallelogram.
4.
A trapezoid is a parallelogram.
5.
The diagonals of trapezoid bisect each other.
6.
A quadrilateral is a trapezoid.
7.
The diagonals of a trapezoid are congruent.
8.
Consecutive angles in a trapezoid are
supplementary.
9.
S
T
N
21.
DOGS is a rectangle. Find the m D .
22.
STAR is a rhombus. The diagonals measure
18 cm and 26 cm.
Find the perimeter of STAR.
Both pairs of opposite sides in a trapezoid are
congruent.
11.
I
Both pairs of opposite angles in a trapezoid
are congruent.
10.
M
x2 and
One pair of opposite sides in a trapezoid are
congruent.
12.
Consecutive angles of a parallelogram are
congruent.
23. GIRL is a rhombus and m 1 37 .
Find the m 2 and m 3 .
Determine if the statement is…
G
3
True or False
13.
All rhombi are squares.
14.
All squares are parallelograms.
15.
All squares are rectangles.
16.
If the diagonals of a quadrilateral are
L
1
2
I
S
1
R
24. PLAY is a kite and LA 12 , RA 8 .
Find LR .
perpendicular, then it is a kite.
17.
L
If the diagonals of a parallelogram are
18.
If the diagonals of a parallelogram are
congruent, then it is a rectangle
12
x
perpendicular, then it is a rhombus.
P
8
R
Y
A
25.
LETS is a trapezoid and GO is a midsegment.
Solve for x.
4x - 13
L
G
29.
E
x
O
S 2x - 7
T
Chapter 8
26.
Use ΔCAR and ΔMEL at below
a.
Find the m A .
b.
Are the triangles similar? Explain why
or why not.
Solve for x in each of the following
proportions.
30.
a.
b.
c.
x
3
In ΔGEM, GO is an angle bisector.
9
10
x
3
4
x 2
6
17
2x
51
a c
, determine if the
b d
other proportions are true or false.
a.
Find the value of x.
b.
Are ΔGOM and ΔGEO similar? Explain
why or why not.
27. Give the proportion
a.
a
d
c
b
b.
a c
b
c c
d
d c
b a
28. Complete the following proportions based on
the diagram.
Determine if the statement is…
True or False
31.
c.
If two polygons are congruent, then they are
similar.
32.
If two polygons are similar, then they are
congruent.
a.
b.
c.
RA
AP
PA
PR
RD
AI
33.
Every polygon is similar to itself.
34.
All rectangles are similar.
35.
All squares are similar.
36.
All equilateral triangles are similar.
37.
All right triangles are similar.
38.
Suppose ΔRUN ~ ΔJOG. Determine if the
statement is true or false.
T
F a. RU and JG are corresponding side.
T
F b.
T
F c. ΔRNU ~ ΔJGO
T
F d.
N and
UN
OG
RN
JG
F e.
RU
JO
T
F
f.
39.
40.
RN
JG
Solve for x.
43.
Solve for x.
G are corresponding angles.
RU
JO
T
42.
OG
UN
Determine if the triangles are similar?
Explain why or why not.
If similar what is the scale factor?
44.
Solve for x.
Determine if the two triangles similar?
Explain why or why not. If similar what is the
scale factor?
Chapter 9
45.
Solve for x. Leave your answer exact.
10
x
2
41.
One triangle has sides 6 cm, 10 cm, and 12 cm
long. Another has sides 15 cm, 25 cm, and
30 cm long. (Hint: Draw a picture. Be sure to
match your corresponding parts.)
a.
Determine if the triangles similar?
Explain why or why not.
b.
If the two triangles are similar, what is
the scale factor of smaller triangle to the
larger triangles?
46.
Solve for x. Leave your answer exact.
x
15
11
47.
Classify the triangle with sides lengths of 7,
12, and 9 as right, acute, or obtuse.
48.
The side length of an equilateral triangle is 24
centimeters. Find the area of the triangle.
(Area = ½ bh)
51.
A new store is being built. An escalator is
planned. It will make an angle of 28˚ with the
floor. If the vertical distance between floors is
14 feet, how long will the escalator be?
Round your answer to tenths.
52.
Solve for x. Round your answer to tenths.
x
38˚
49.
Find the perimeter of the figure. Leave your
answer exact.
22
12 ft
53.
45˚
50.
Solve for x. Leave your answer exact.
Find m X . Round your answer to nearest
degree.
Z
X
40
54
x
16
Y
54.
60˚
Chapter 10
55.
Identify the following in the diagram.
a. Name a radius: __________
b. Name a diameter: ________
c. Name a chord: _________
d. Name a tangent line: ________
You want to find the height of a building.
You stand 100 feet away from the building
and measure the angle of elevation to be 30˚.
How high is the building? Round your answer
to tenths.
56.
Use the circle at the right to answer questions 56. EB and AD are diameters
a. Find mBC .
________
b. Find mCD .
________
c. Find mCAE
________
Find the indicated variable(s) for each diagram.
57.
Find x
58.
Find x
59.
mLNM = 280˚,
find y.
60.
Find a and b.
61.
Find x and y.
62.
m ABC = (12x + 20)
m ADC = (11x – 1) .
Find x.
B
A
C
D
63.
Find x
64.
Find the m D .
65.
Find x
F
x
90
86
E
30
x
O
30
D
H
G
120
66.
Find x.
67.
Find m BEC
A
68.
Find x
68˚
x
B
5
x
2
1
2
2
E
4
6
D
C
126˚
69.
Find x.
70.
Find DB
190º
A
10
xº
B
C
58º
71.
Find HO.
O
(x - 6)
U
4
x
D
84º
72.
6
Find mUH
H
3
N
H
U
x
(6x + 18)º
48º
D
M
30º
E
73.
Graph the circle with a
radius of 4 and a center
of (6, -3).
74.
Graph the circle,
(x - 2)2 + y2 = 4
76.
Find the measure of each numbered angle given the picture.
a. m 1 ________
75.
110
E
˚
b. m 2 ________
2
3
c. mED ________
d. m 4 ________
e. m 5 ________
Determine the equation of
the graph below.
A
F
1
6
7
8
4
D
AD is a diameter
f. m 6 ________
h. m 8 _______
86˚
G
g. m 7 ________
B
5
C
ANSWERS
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
A
S
A
N
N
S
S
S
N
N
S
S
F
T
T
F
T
T
44 2 u.
50 u. or 98u,
90
20 10 u.
23.
m 2 37 and
m 3 53
4 5 u.
5
27
a.
10
b.
6
c.
9
a.
F
b.
F
c.
T
DI
a.
IP
PI
b.
PD
PD
PR
c.
or
PI
PA
70
a.
b.
Yes, AA~
a.
7.5
b.
No.
T
F
T
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
F
T
T
F
a.
b.
c.
d.
e.
f.
62.
63.
64.
65.
F
T
T
T
T
F
3
5
Yes, SAS~,
40.
No, sides not
proportional
a.
Yes, SSS~
2
b.
(order matters)
5
10
24
14
2 30
2 26
Obtuse
144 3
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
55.
72.
73.
74.
204
See class key
See class key
66.
39.
41.
71.
7
60
28
240
11
4
83
4
15
50
3
HO 11 u.
24 2 12
8 3
29.8 ft
28.1
48
100 3
or 57.7 ft
3
a.
EB, EF , or EG
b.
c.
FB
FB or CG
d.
AJ or HJ
56.
a.
b.
c.
35
90
215
57.
58.
59.
60.
61.
34
22
40
a 50 and b 25
x 48 and y 42
67.
68.
69.
70.
75.
76.
x 3
a.
b.
c.
d.
e.
f.
g.
h.
2
35
47
70
55
55
98
47
43
y 5
2
16