Name___________________________
1.
Unit 5 Review
Given the diagram to the right solve for the following:
a.) x
b.) y
If 𝛥𝐴𝐵𝐶 ~ 𝛥𝐴′𝐵′𝐶′, then the sides must be in ____________________
corresponding angles must be _____________.
C'
to each other and the
12
6
C
4
A
5
B
A'
B'
6
a.)Find the missing sides in the two triangles.
b.) If ∠A=20°, then ∠A’=__________
3. Given the diagram below and ∆𝐴𝐵𝐶~∆𝑋𝑌𝑍, Find the lengths .
7x
5x
x
14
4. In the triangle shown segment AB is an angle bisector to angle A.
H
5
Solve for x
x
B
8
K
A
12
5. The vertical lines shown in the diagram below are parallel, solve for x.
6. In right triangle 𝐴𝐵𝐷, 𝐴𝐵 = 15, and altitude 𝐷𝐶 = 6. Find the length of BC.
6
0
15
7. If the ratio of corresponding sides of similar triangles is 2:7 what is:
a. The ratio of their perimeters?
b. The ratio of their areas?
c. If a side of the smaller triangle is 6, what is the corresponding side of the larger triangle?
d. If the Perimeter of the larger triangle is 45.5, what is the perimeter of the smaller triangle?
e. If the Area of the smaller triangle is 24, what is the area of the larger triangle?
8. Use the diagram below to answer the following questions.
a.
State the pair of similar triangles.
A
18
b.
Which similarity criterion guarantees their similarity? (AA, SAS, SSS)
D
3
c.
Calculate 𝐴𝐵 to the nearest hundredths place.
7.25
C
5
E
30
B
9. The triangles shown below are similar.
a.) What is the ratio of the sides?
y
3
1.25
b.) What is the ratio of the Perimeters?
x
15
c.) What is the ratio of the Areas?
10.5
d.) Solve for x
e.) Solve for y
10. Use the picture below to answer the following questions
a. If you know two sides of a right triangle, how do you find the third side?
b. What proportions can be used to find missing parts in the diagram below?( Write it in words)
c. Solve for x, h and y
x
h
4
13
11. Two legs of a right triangle are 5 and 10, find the perimeter of the triangle, and write your answer in simplest
radical form.
12. Sally who is 5ft tall casts a shadow that is 4ft long, at the same time a nearby flag pole casts a shadow that is 7ft
long, how tall is the flag pole?
13. Use the picture below to answer the following questions (BE || AT):
f.
If BC= 3, CE=4 , ET=6 , what is BA?
g. If CB= 6, CA=18 , CE=5, What is ET?
h. If CB=7, BA=14,BE=10, What is AT?
i.
Explain why you can’t use the side splitter theorem for part c.