Chapter 11 Test Review Packet
Name_______________________________Period__________
For 1-4, the given figures are similar. Find the missing measurement(s)
1.
2.
3.
4. ∆𝐴𝐵𝐶 ~ ∆𝐷𝐵𝐴
For 5-8 state whether each pair of polygons is similar. Explain why or why not.
5.
6.
7.
8.
∆𝐴𝐵𝐶 ~ __________
9.
A building cast a shadow that is 420 meters
long. At the same time, a person who is 2
meters tall casts a shadow that is 24 meters
long. How tall is the building?
10.
11. Find x.
Johnny wanted to know if he could dunk a
basketball. To figure this out, he needed to know
how tall the hoop was. So, he placed a mirror on
the ground so that when he looked into the mirror,
he saw the top of the hoop. The mirror was 5 ft
from his feet and 8 ft from the base of the goal. If
Johnny’s eyes are 6 ft above the ground, how tall is
the hoop?
12.
13. Find x.
13
14.
Find the missing value.
16. Find x
15. Find the missing value.
17.
19.
18.
a. The ratio of the corresponding midsegments of two
similar trapezoids is 4:5. What is the ratio of their areas?
b. The ratio of the areas of two similar pentagons is 4:9.
What is the ratio of their common sides?
20. The two prisms are similar.
21.
Dogs and Wolves both belong to the same
family. Assume their bodies are similar. A dog
is typically 4 feet long, while a wolf is about 6
feet long. What is the ratio of the surface area
of the dog to that of the wolf? What is the
ratio of their volumes?
22. If the two isosceles trapezoids are similar, what is the
area of the larger trapezoid? What is the perimeter?
23.
1.2 in.
6 in.
5 in.
48 in.2
A = ________
P=
2 in.
24. The ratio of the areas of two similar figures is 49:144. What is the ratio of their volumes?
25.
26.
x = ____________
x
13
15
y = ____________
15
x
y = ____________
24
y
10
y
5
x = ____________
27. Decide whether the statement is true or false. If the statement is false, correct the statement or provide a
counterexample.
a._____ All isosceles triangles are similar
b._____ If two sides of one triangle are proportional to two sides of another triangle, then the triangles are
proportional.
𝑎2
𝑎
c._____ If two cylinders have heights in the ratio 𝑏 , then their volumes are in the ratio 𝑏2 .
d.____ If two triangles are similar, then the corresponding angle bisectors are proportional to the
corresponding sides.
e._____ Two polygons are similar if and only if corresponding angles are congruent and corresponding sides are
congruent.
f._____ The 3 triangle shortcuts for similar triangles are AA, SSS, AAS.
g._____ Indirect measurement is the process of using similar triangles to calculate the height of tall objects that
can’t be reached.
h._____ All circles are similar.
28. Name 4 figures that are ALWAYS similar.
29. Name 4 figures that are NOT NECESSARILY similar.
30. Find the geometric mean between 8 and 16.
31.
x = ____________ y = ____________
C
B
14
x
E
y
28
20
16
D
A
32. Sketch a picture and fill in the blank: _____________________________ in a triangle divides the opposite side
into the same ratio as the other two sides of the triangle. SKETCH A PIC HERE:
33. READ OVER YOUR CHAPTER 11 VOCAB/CONJECTURES and review the following topics for the Chapter 11 Test:
a) Decide whether the 3 side lengths of a triangle form a right, acute, or obtuse triangle
b) Special right triangles (45-45-90 and 30-60-90)
c) Volume of a sphere and hemisphere