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Apply Properties of Similar Polygons. VII-3. Similar Polygons. If two polygons are similar, their corresponding angles are congruent and the lengths of corresponding sides are in proportion.

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Presentation Transcript
similar polygons
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
proportions
Proportions
  • Two ratios (fractions) that are equal to each other are called proportions.
  • Example:
solving proportions
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

slide5

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

slide6

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

slide7

E

F

A

B

ABCD~EFGH. What is the value of y?

  • 12
  • 14
  • 15
  • 16

y

12

10

8

D

C

H

16

G

Answer: C

slide12

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

slide13

Answer: D

If the triangles are similar, then corresponding sides are proportional.

Find corresponding sides.

slide15

Answer: D

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

slide16

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