Chapter 11 Similarities
Review Notes:
To solve a proportion I need to _______________________
To be similar, sides are____________________ and angles are________________
Dilations are ________________
What are the three similarity shortcuts for triangles:__________________________
If two triangles are similar, what corresponding parts are proportional?
Solve each proportion.
1)
d
72

22 32
2)
x
x2

20
28
3) If a car can travel 320 miles on 16 gallons 4) Are rectangles KLMJ and BCDA similar?
of gas, then how many gallons of gas is
Explain why or why not.
needed to travel 220 miles?
5) Are these triangles similar? If so why?
15º
6) STU ~ VWX. Find x.
120º
45º
120º
7) ABCD ~ EFGH. What is the length of
AB?
8) Given that m<A  m<D and m<C  m<F, find
x and y.
9) ABCDEF ~ GHIJKL. Find JK if DE = 12
mm, BC = 14 mm and HI = 7mm.
10) ∆ BAE ~ ∆HIE. Find x.
11) Find y.
12) ∆ SKI ~ ∆JMP. Find x.
13) Given that AE || BD, find x.
14) Is PQ || BC ? Explain.
15) A yardstick casts a shadow 2ft long at the same time a tree casts a shadow 32 ft long.
How tall is the tree, to the nearest foot?
16) If the areas of two similar cylinders are
16
in the ratio , then their volumes are in
9
what ratio?
17) The ratio of the corresponding volumes
of two similar pentagonal prisms is 343:27.
What is the ratio of their heights and
areas?
18) The ratio of the corresponding
midsegments of two similar trapezoids is
4:5. What is the ratio of their areas?
19) The ratio of the areas of two similar
pentagons is 4:9. What is the ratio of their
corresponding sides?
20) PORT ~ LAND. Find OR.
21) The area of circle Q is 72 cm2. Find
the area of circle R if
Area of PORT
9

Area of LAND 16