1. Apply Properties of Similar Polygons
VII-3

2. Similar Polygons
If two polygons are similar, their corresponding angles are congruent and the lengths of corresponding sides are in proportion.
To set up proportion correctly, it is important to keep the measurement of each polygon on opposite sides of the equal sign.
Symbol ~ means similar

3. Proportions
Two ratios (fractions) that are equal to each other are called proportions.
Example:

4. Solving Proportions To find a number missing (x) from a proportion:
First multiply the two numbers that are diagonal
Then divide the product by the other number in the proportion
Example:
5x = 120
x = 24

5. In the diagram below, ABCD and EFGH are similar
In the diagram below, ABCD and EFGH are similar. What is the length of AD?
A 5
B 6
C 9
D 12 F G B C 3 9 A D E H 15
Answer: A

6. In photography, the shape of the final picture is similar to the shape of the negative. What will be the width of the final picture made from the negative shown in the diagram below?
7.2 centimeters
14 centimeters
15 centimeters
20 centimeters
Picture
Negative
3 cm
12 cm
5 cm
Width = ?
Answer: D

7. ABCD~EFGH. What is the value of y?12 14 15 16 E F A B y 12 10 8 D C H 16 G
Answer: C

8. Triangles ABC and RST are similar. What is the value of c?9 12 15 24 B S a c 4 3 R T A C 6 18
Answer: B

9. Answer: C

10. If ABCDEFGH MNPQRSTU, what is the length of segment TS?
Answer: B

11. Answer: B

12. In the patio plan shown below, figure ACE is similar to figure BCD
In the patio plan shown below, figure ACE is similar to figure BCD. What is the length of segment AE? a. 3 feet b. 5.3 feet c. 9 feet d. 15 feet
Answer: C

13. Answer: D
If the triangles are similar, then corresponding sides are proportional.
Find corresponding sides.

14. If DXYZ ~ DRST, which of these proportions is true?
Answer:

15. Answer: D
If you multiply the given dimension (2 x5) by 3, you get (6 x 15)

16. a. 7 centimeters by 12 centimeters b. 8 centimeters by 28 centimeters
Which of these dimensions form a rectangle similar to a rectangle with a width of 2 centimeters and a length of 7 centimeters?
a. 7 centimeters by 12 centimeters
b. 8 centimeters by 28 centimeters
c. 4 centimeters by 49 centimeters
d. 3 centimeters by 14 centimeters
Answer: B

17. Answer: C

18. Answer: C