Name: ______________________
Block: _______
Date: ________
Use the diagram to complete the statement.
1. ∆ ABC ~ ____
2. BA  AC  CB
(which thm/post proves this?)
3. 25 
12
5. y  ____
4.
25

18
6. x  ____
Determine whether the triangles are similar. If they are, state the theorem or postulate use
and write a similarity statement. If they are not similar, state “Not Similar.”
7.
8.
thm/post: ______ _______ ~ _______
thm/post: ______ _______ ~ _______
9.
10.
thm/post: ______ _______ ~ _______
thm/post: ______ _______ ~ _______
11.
12.
13.
thm/post:
thm/post:
thm/post:
_______ ______~ ______
_______ ______ ~ ______
______
*You might find
it helpful to draw
∆LQN and ∆MPN
separately
*You might find
it helpful to
draw ∆ACE and
∆BCD separately
_____ ~ _____
14. In the diagram, AB DC , AE = 6, AB = 8, CE = 15 and DE = 10.
a. List two pairs of congruent angles in the diagram.
Hint: Find a pair of vertical angles
 ____   ____
Hint: Find a pair of alternate interior angles created by
a transversal of the parallel lines  ____   ____
b. Find a pair of similar triangles and write
a similarity statement.
______
_______
c. Write a statement of proportionality for the sides:
AB
CD


d. Find BE and DC. Plug known lengths into the statement of proportionality to set up your
equations.
15. Is either ∆JKL or ∆RST
similar to ∆ABC?
16. Ruby is standing in her back yard and she decides to estimate the height of a tree. She stands
so that the tip of her shadow coincides with the tip of the tree’s shadow, as shown. Ruby is 66
inches tall. The distance from the tree to Ruby is 95 feet and the distance between the tip of the
shadows and Ruby is 7 feet.
a. What postulate or theorem can you use to show that the
triangles in the diagram are similar? _________
b. About how tall is the tree, to the nearest foot?