Chpt 3-4 Review Worksheet

Name:_______________________________________________________
Period:__________
Secondary Math II - Review Packet for Chapter 3 and 4
Determine whether it is possible to form a triangle using segments with the following measurements. Show
all your work.
1. 14 inches, 21 inches, 7 inches
2. 26 feet, 10 feet, 18 feet
3. 2.2 millimeters, 7.2 millimeters, 5.1 millimeters
Find the missing angle.
W
4.
5.
119 ̊
37 ̊
X
M
N
40 ̊
108 ̊
Y
O
W
Solve for the variable.
6.
(2x + 5 ̊ )
7.
3x
95 ̊
(5x – 1 ̊ )
(8x + 5 ̊ ) ̊
(9x – 7 ̊ )
8. Given a triangle with two sides measuring 6 inches and 14 inches, what are the possible dimensions of
the third side, x?
9. Given a triangle with two sides measuring 10 cm and 30 cm, what are the possible dimensions of the
third side, r ?
10. List the angles of each triangle shown in order
from least to greatest.
⊿𝑈𝑃𝑀 =
P
I
35 ̊
21 ̊
⊿𝑃𝑀𝐼 =
11. List the sides of the triangles shown in order
from least to greatest.
M
63⁰
U
List the angles and sides of each triangle in order from least to greatest without measuring.
P
B
12.
13.
101 ̊
60 ̊
B
32 ̊
57 ̊
C
A 63 ̊
47 ̊
U
Y
14.
R
15.
10 cm
7 cm
16 cm
7 cm
Z
X
T
S
21 cm
Calculate the missing or unknown side lengths of each triangle. Leave your answers in square root form, or
round your answers to the nearest tenth. Show all your work.
16.
17.
15 yards
c
11 in.
30 yards
a
9 in.
18.
19.
16 ft 45 ̊
c
45 ̊
a
a
45 ̊
b
45 ̊
32 cm
20.
21.
c
30 ̊ ̊
8 mm
a
30 ̊
c
b
60 ̊ ̊
5 ft
22.
23.
b
a
b
2.2 mm
60 ̊ ̊
60 ̊ ̊
c
14 ft
24.
25.
x
18 cm
a
x
30 ̊
c
24 yds
Determine if the triangles are similar. If they are similar, state how you know (by which similar theorem.)
AND Determine the scale factor if possible.
E
26.
1.5 cm
F
6 cm
27.
G
60 ̊
7 cm
14 cm
A
C
85 ̊
3 cm
B
12 cm
35 ̊
85 ̊
M
28. J
16 in
29.
28 in
L
8 in
8 cm ̊ ̊
21 in
12 in
50 ̊
12 cm
7.5 cm ̊
50 ̊
K
5 cm ̊ ̊
O
N
14 in
30.
10 mm
20 mm
31.
32.
4.5 ft
38 ̊
6.75 ft
40 ̊
35 ̊
35 ̊
3 ft
40 ̊
4.5 ft
102 ̊ ̊
33. KN bisects angle K. Calculate MN.
34. SQ bisects angle S. Calculate SR.
L
S
35 m
14 m
13 in
K
N
16 m
M
R
T
9 in
r
Q
10 in
Use the Triangle Proportionality Theorem and the Proportional Segments Theorem to determine the value
of x.
35.
B
B
36.
3
4.6
C
C
x
x+5
A
5.3
D
E
12.9
x-1
A 1
E
C
37.
B
A
E
D
Given: ABC is a triangle.
B is the midpoint of AC
E is the midpoint of AD
The Length of BE is 9. What is the length of CD?
38. You want to measure the height of a tree at the community park. You stand in the tree’s shadow so that
the tip of your shadow meets the tip of the tree’s shadow on the ground, 2 meters from where you are
standing. The distance from the tree to the tip of the tree’s shadow is 5.4 meters. You are 1.25 meters
tall. Draw a diagram to represent the situation. Then, determine the height of the tree.
39. Given triangle HJK with vertices of H(2, 6), J(2, 10), K(7, 3), what are the vertices of the image after a
dilation with a scale factor of 4 using the origin as the center of dilation?
40. What is the midpoint between
(7, -5) and (3, -1)?
41. What is the midpoint between
(-14, 8) and (6, -4)?
D
42.
Stacy wants to know the height of the cell phone tower. She places a small mirror on the ground
between herself and the cell phone tower, then she backs up until she can see the highest point of the
tower in the mirror. The diagram illustrates Stacy’s measurements. What is the height of the cell
phone tower?
5 ft
I----------80 ft-------------------------I--10ft-I
43. Given triangle HJK with vertices of H(2, 6), J(2, 10), K(7, 3), what are the vertices of the image after a
dilation with a scale factor of 4 using the origin as the center of dilation?
44. Find the distance between (7, -5) and (3, -1).
45. Find the distance between (-14, 8) and (6, -4).
46. On a separate piece of paper, define and draw a picture of:
A.) Adjacent Angles
F.) Alternate Exterior Angles
B.) Vertical Angle
G.) Alternate Interior Angles
C.) Linear Pair
H.) Same-Side Exterior Angles
D.) Complementary Angles
I.) Same-Side Interior Angles
E.) Supplementary Angles
J.) Corresponding Angles
47. Explain Inductive Reasoning and give an example:
48. Explain Deductive Reasoning and give an example:
49. Rewrite the following phrase in the different forms indicated: “The angles are supplementary, so the
sum of their measures is 180°.”
A.) Conditional:
B.) Converse:
C.) Inverse:
D.) Contrapositive:

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