Chapter 11 Review Packet
Name_______________________________Period__________
For 1-5, the given figures are similar. Find the missing measurement(s)
1.
2.
120°
x
z
27
c°
y
3.
4.
∆𝐴𝐵𝐶 ~ ∆𝐷𝐵𝐴
5.
x
45
20
For 6-9 state whether each pair of polygons is similar. Explain why or why not.
6.
7.
by _______
8.
by _______
9.
∆𝐴𝐵𝐶 ~ __________ by _______
10. 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?
12. Find x.
11.
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. He stood 5 ft from the
mirror and 13 ft from the base of the goal. If Johnny
is 6 feet tall, how tall is the hoop?
13.
14. Find x.
12
13
15.
Find the missing value.
16. Find the missing value.
x
17. Solve for the missing variable(s). Round to the nearest tenth if necessary.
a.
b.
c.
x
18.
19.
Find the geometric mean between the given numbers:
a. 8 and 18
b. 35 and 7
20.
a.The ratio of the corresponding midsegments of two
similar trapezoids is 4:5. What is the ratio of their areas?
21.
b. The ratio of the areas of two similar pentagons is 4:9.
What is the ratio of their bases?
c. The ratio of the volumes of two spheres is 64:125. What
is the ratio of their surface areas?
22.
23.
24. If the two isosceles trapezoids are similar, what is the 25.
area of the larger trapezoid? What is the perimeter?
6 in.
1.2 in.
5 in.
48 in.2
2 in.
A=
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?
26.
27. Solve for x and y.
21
x
15
C
B
10
12
x
E
24
10
y
18
A
D
28. The dimensions of a small pyramid are onethird the dimensions of a larger pyramid. If
the volume of the larger pyramid is 540 cm3,
what is the volume of the smaller pyramid?
29. ∆ABC
∆DBA, find x + y:
18
12
10
30. 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.
𝑎
𝑏
c._____ If two cylinders have heights in the ratio , then their volumes are in the ratio
𝑎2
.
𝑏2
d.____ If two triangles are similar, then the corresponding angle bisectors are proportional to the
corresponding sides
e.____ An altitude of a triangle divides the opposite side of the triangle into two segments whose lengths are in
the same ratio of the lengths of the two sides forming the angle.
f.____ All spheres are similar
g.____ If a line passes through a triangle parallel to one of the sides, then it splits the other two sides
congruently.
31. Draw and label an example of each conjecture:
a. If a line passes through two sides of a
triangle, dividing them proportionally,
then the line is parallel to the third side.
b. An angle bisector in a triangle divides
the opposite side into the same ratio
as the other two sides of the triangle.
32. There will be 4 mixed review questions on the Chapter 11 test. You will want to study the following:
a. Using the Converse of the Pythagorean Theorem to determine if a triangle is right, acute, or obtuse.
b. 30-60-90 and 45-45-90 Special Right Triangles (Section 9.3).
c. Calculating volume if given a formula