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Apply Properties of Similar Polygons

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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Apply Properties of Similar Polygons

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  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. 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. 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

  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? a. 32 b. 4 c. d. Answer: B

  11. Answer: B

  12. 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. 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

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