# Dilations &amp; Similarity #1

```Name _________________________________ Period_________ Date________________
Dilations &amp; Similarity #1
1. What does similarity mean? ______________________
2. What does the symbol ∼ mean? _________________________
y
5
A′
3. Name the transformation(s) that show that
ABC ABC .
A
x
4. Using the Pythagorean Theorem, find the measurement
̅̅̅̅̅.
̅̅̅̅ and 𝐴′𝐶′
of 𝐴𝐶
B′
B
C
C′
-5
-5
5
5. Replace the side lengths that correspond to each segment to show the ratios are proportional.
AB AB

BC BC 
AC AC 

BC BC 
AB AB

AC AC 
6. The pair of triangles in the figure is similar. What is the value of x?
20 in.
x
3 in.
y
4 in.
Proportion _______________
16 in.
7. Using the same figure above, what is the value of y?
Proportion _________________
Solution__________
Solution____________
̅?
8. ∆ 𝐽𝐾𝐿 is similar to ∆ 𝑅𝑆𝑇. What is the value of 𝐽𝐿
J
R
10
Proportion _______________
K
L
10
S
Solution____________
T
8
̅̅̅̅ = 15, 𝐴𝐶
̅̅̅̅ = 9, 𝑎𝑛𝑑 𝐴𝐷
̅̅̅̅ = 5, then find 𝐴𝐹
̅̅̅̅ .
9. ∆ 𝐴𝐵𝐶 ~∆ 𝐴𝐷𝐹 (~ means “similar to”). If 𝐴𝐵
A
D
F
Proportion _________________
B
Solution__________
C
10. Polygon 𝐴𝐵𝐶𝐷 is similar to polygon 𝐸𝐹𝐻𝐺. Using the values in this diagram, find x.
20
A
B
15
E
F
x
y
12
H
G
Proportion _________________
D
10
Solution__________
C
11. Using the diagram above, find the value for y.
Proportion _________________
Solution__________
12. At the same time of day, a man who is 6 feet tall casts an 8-foot shadow and his son casts a 4 foot shadow.
What is the height of the man’s son?
Proportion _________________
Solution__________
13. Draw two similar quadrilaterals and label the sides and the angles to show they are similar.
```