This document contains a worksheet with 6 problems involving similar triangles. The first problem contains two similar triangles with missing side lengths x and y. The second problem asks the reader to find x if two specified triangles are similar. The third and fourth problems involve setting up and solving proportions between corresponding sides of similar triangles. The fifth problem contains a "tricky" proportion involving addition. The sixth problem uses similar triangles formed by a pole, man, and their shadows to find the height of the pole.

1. Worksheet: Similar Triangles Worksheet: Similar Triangles
1. In the triangle pair below, ∆ABC ~ ∆DEF . 1. In the triangle pair below, ∆ABC ~ ∆DEF .
A D A D
12 15 8 x 12 15 8 x
B C E F B C E F
y 9 y 9
x = _____ y =______ x = _____ y =______
F F
2. A 12 2. A 12
9 9
x x
4 4
B B
8 8
C C
E E
If ∆ABC ~ ∆EBF then x=____ If ∆ABC ~ ∆EBF then x=____
x 12 x 12
3. Solve: = 3. Solve: =
8 15 8 15
4 12 4 12
4. Solve: = 4. Solve: =
5 x 20 5 x 20
x+2 3 x+2 3
5. Solve: = (watch out! Tricky!) 5. Solve: = (watch out! Tricky!)
3 15 3 15
6. 6.
20 feet 12 feet 20 feet 12 feet
A rooster is sitting at the top of a pole. A rooster is sitting at the top of a pole.
A man, who is 5.5 feet tall, wants to climb A man, who is 5.5 feet tall, wants to climb
the pole to do the rooster harm (the bird the pole to do the rooster harm (the bird
wakes him up at 3 A. M. every morning). wakes him up at 3 A. M. every morning).
If the pole and the man both cast a shadow If the pole and the man both cast a shadow
and the lengths are shown, find then height and the lengths are shown, find then height
of the pole. __________ of the pole. __________