Name __________________________________________________
Date _________________________
Period ________
Similarity Review
Solve each proportion. Show all work. Leave answers as reduced fractions when necessary.
𝟓
𝟏𝟑
𝟐𝒙+𝟔
𝟒
𝟕
𝟐𝒙+𝟏
𝒙−𝟒
1.
=
2.
=
3.
=
4.
𝒙
𝟐𝟔
𝟏𝟎
𝟑
𝟔
𝟐𝒙
𝟖
=
𝟐
𝒙+𝟐
Use a proportion to solve the following problem. Include correct units in your proportion and answer.
5. Suppose you walk 2 miles in 35 minutes. How far could you walk in an hour if you were to continue at the
same rate? Hint: How many minutes are in one hour? Round your answer to the nearest hundredth if
necessary. (decimal answer)
6. ABCD~FGHI. Find the value of each variable.
w=__________
x=__________
y=__________
z=__________
Are the following polygons similar? Show all work to support your answer. Explain why or why not.
7.
8.
YES or NO (circle one)
Why or why not? ______________________________
YES or NO (circle one)
Why or why not? __________________________
_____________________________________________
__________________________________________
_____________________________________________
__________________________________________
Are the triangles below similar? If so, write the similarity statement, and name the conjecture that you
can use to prove they are similar. If no, write “Not Similar” and explain why not. Show all work and/or
necessary markings.
10.
9.
Similarity Statement: ∆𝐿𝑈𝑉~∆_________
Similarity Statement: ∆𝐽𝐾𝐿~∆_________
Reason:____________________________
Reason:___________________________
Why are the triangles similar in each example below? Use a proportion to find the value of the 𝒙 in each
problem. Show all work.
11. Round to nearest hundredth.
12.
𝑥 = __________
𝑥 = __________
13. ∆𝑨𝑩𝑪~∆𝑫𝑩𝑨. Write proportions to find the value of the variables in each problem below.
Round to the nearest tenth. Show all work. Redraw triangles and color-code each pair of
corresponding sides using the similarity statement.
25
7
𝒙
𝑥 = __________
𝑦 = __________
14. First redraw and label the triangles in the following diagram below. Write proportions to find the
value of the variables in each problem below. Show all work.
*Redraw Triangles:
𝑥 = __________
𝑦 = __________
15. Sally is 5 feet tall and casts a shadow that is 4 feet long. At the same time, a tree casts a shadow that is
20 feet long. How tall is the tree? Draw and label a diagram.
Diagram:
Height of tree: __________________
16. In sunlight, a vertical yardstick casts a 1-ft shadow at the same time that a nearby tree casts a 15-ft shadow.
How tall is the tree?
17. A man 6 ft. tall wishes to find the height of an oak tree in his front yard. He walks along the shadow of the tree
until his head is in a position where the end of his shadow exactly overlaps the end of the treetop’s shadow. He
is now 11 ft. from the foot of the tree and 8 ft. from the end of the shadows. How tall is the oak tree?
#18-21: Find the value of x.
18.
19.
22. Find the value of x and y.
(Round to nearest tenth)
20.
23. Triangles are similar
21.
24. Triangles are similar
25. The corresponding sides of two similar trapezoids have a ratio of 3:5. If the area of the smaller is 63 sq. in., what
is the area of the larger?
26. Two cubes have edges in the ratio of 4:3.
a. What is the ratio of their surface areas?
b. What is the ratio of their volumes?
27. The ratio of the weights of two spherical balls is 27:64.
a. What is the ratio of the diameters of the two balls?
b. What is the ratio of their surface areas?
28. Two similar cylinders have surface areas in the ratio of 36:25. What is the ratio of their volumes?
#29-34: Solve each problem for the following similar figures.
29. Find the ratio of the areas.
30. Find the area of the
31.
larger triangle.
32.
33. Are the rectangular
prisms similar?
34. Are the right cylinders
similar?