Use the triangles to answer the questions. Triangle ABC is similar to triangle DEF.
A C
B
4.5
6
5.1
E F
D
4.25 3.75
5
Fill in each blank with the correct angle.
1) ∠A ≅
2) ∠B ≅
3) ∠C ≅
Show that the two triangles are similar by creating proportions for the corresponding sides. Then,
substitute in the given values and simplify the cross products for the equivalent ratios.
4) Proportion for side AB
BC and the corresponding ratio from DEF :
Substitute values and simplify cross products.
5) Proportion for side BC
CA and the corresponding ratio from DEF :
Substitute values and simplify cross products.
6) Proportion for side CA
AB and the corresponding ratio from DEF :
Substitute values and simplify cross products.
Use the triangles to answer the questions. Triangle JKL is similar to triangle MNO. Find the
values of x and y so the corresponding sides are proportional.
K
0.3
J L x
0.5
O
M N
9
y
12
7) Set up the three proportions for the corresponding sides. Write the ratios between the two
figures. Start at vertex J and work clockwise. Then, write the proportions with the correct
substituted quantities. The first proportion is started for you.
a. First proportion b. Second proportion c. Third proportion

JKL
MNO
JK
OM → =
= 0 3.
y
8) Solve the proportion to find the value of x.
9) Solve the proportion to find the value of y.
10) Confirm the values for x and y by testing the equivalent ratio that includes both variables.
Use the situation and the figures to answer the questions.
The figures below show the ramps to two loading docks that are manufactured in the shapes of
similar triangles. What is the length of the longer ramp?
11) Set up a proportion with r representing the unknown length. Let the diagonal side lengths
be the numerators.
12) Solve the proportion for the unknown. Show all work. State the solution in a complete
sentence using appropriate units.
Work:
Solution:
Show that the two triangles are similar by using the AA method.
78°
37°
A C D F
B
E
13) Find the measure of ∠A : m∠ =A
14) Find the measure of ∠E : m∠ =E
m F ∠ =
Work:
x16) State why ∆ABC and ∆DEF are congruent using the AA method.



Standardized aSSeSSment Practice
Choose the correct answer.
17) The two shapes are similar triangles. Which of the following proportions is NOT true?
4.256
2.34
13.25
7.8
x
y
A. 78 234
4 256
. .
x . = B. 13 25
7 8
.
x .
y = C.
x
13 25 y
4 256
.
. = D.
13 25 7 8
2 34