14K
26A
18T
=
55
Similar Triangles Review Assignment
1.
The following pairs of triangles are similar. State the pairs of corresponding angles and
sides. (4K)
A
F
G
120°
C
B
D
J
120°
H
E
2.
Determine whether △CED is similar to △FHG (4A)
F
C
61.2
15.3
10
40
D
E
13.5
H
54
H
3.
For each pair of triangles, find the measures of the remaining sides.
△LMN is similar to △YXZ (6K)
X
M
l
n
L
y
z
m
N
Y
x
Z
a) l=24, m=30, n=5, x=16
b) l=9, x=6,
y=8, z=4
c) l=4.59, m=6.00, n=3.75, x=4.00
4.
To determine the height of an old building, a surveyor obtains these measures. The
building’s shadow is 12m long. At the same time, a 3-m tall tree has a 2-m shadow.
How tall is the building? (3T)
5.
According to a city by-law, backyard trees cannot be taller than 10m. Harold needs to
determine if he must prune the maple tree on his property. His tree casts a shadow which
is 6 m long. A 4-m tall post is held so that it is in line with the top of the tree and casts a
shadow of 2m. How tall is the tree? Does it need pruning? (4T)
6.
Using the Pythagorean Theorem, calculate the length of the missing side. (4K)
a)
12, 16, c
b)
7, b, 15
c)
a, 15, 22
d)
8,b,10
7.
A school is erecting a new flagpole. The pole is supported by a 5-m guy wire anchored 2
m from the base of a pole. How tall is the pole? (3T)
Guy wire
5 m
Pole
2 m
Given △ABC is similar to △DEF
8.
a) draw △DEF with side DE = 12.0
b) find the length of each unknown side
c) Find each unknown angle
(6A)
A
6.0
3.2
70
B
9.
30
C
6.3
For the triangle below, find the lengths of QT, QR, and PR. (6A)
P
10
6
T
Q
3
S
‘
12
R
10.
A triangular sign has sides of length 2.0m, 5.0m and 6.3 m. In a photograph of it, the
smallest side is 1.5 cm long. How long are the other sides? (4A)
11.
How wide is the base of the triangle (DE)? (3A)
E
D
100m
60 m
B
C
75m
90 m
A
12.
Carlos is trying to determine the height of a mature tree. A young tree’s height is 5.0 m
and it casts a 2.0 m shadow. At the same time, the mature tree casts a 3.5 m shadow.
How all is the mature tree? (4T)
13.
A 3.0 m ladder is leaning against a wall. The foot of the ladder is placed 0.8m from the
base of the wall. How high up the wall does the ladder reach? Write your answer to one
decimal place. (4T)