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Similar Polygons

Similar Polygons. What are similar polygons?. Two polygons are similar if corresponding (matching) angles are congruent and the lengths of corresponding sides are proportional. Angles and Sides in Similar Polygons. Angles ∠A ≅ ∠ E ∠B ≅ ∠ F ∠C ≅ ∠ G. Sides AB ~ EF AC ~ EG BC ~ FG. A.

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Similar Polygons

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  1. Similar Polygons

  2. What are similar polygons? Two polygons are similar if corresponding (matching) angles are congruent and the lengths of corresponding sides are proportional.

  3. Angles and Sides in Similar Polygons Angles ∠A ≅ ∠ E ∠B ≅ ∠ F ∠C ≅ ∠ G Sides AB ~ EF AC ~ EG BC ~ FG A ΔABC ~ ΔEFG E B C F G

  4. You can find the missing length of a side in a pair of similar figures, by using proportions ΔRST ~ ΔUVW R x ft. U 6 ft. S T W V 35 ft. 7 ft. 6 7 x = 30 feet = x 35

  5. Solve for x. 40 in. 30 in.. 12 in. x in. x 30 x = 9 inches = 12 40

  6. Solve for x. Round to the nearest tenth. 12 in. 4 in. 20 in. x in.. 4 x x = 6.7 inches = 12 20

  7. Solve for x. x 25 m. 14 m. 7 m. 7 25 x = 50 meters = 14 x

  8. Solve for x. Round to the nearest tenth. 17 in. x 35 in. 15 in. 15 x x = 7.3 inches = 35 17

  9. What is the scale factor of the figure? WX 15 3 = = PQ 10 2 YZ 9 3 XY 6 3 = = = = RS 6 2 QR 4 2 WX 15 3 = = So, the two figures are similar and the scale factor is 3:2. PQ 10 2

  10. Patterns and Sequences • Can you find the pattern? • 1, 2, 4, 8, 16, ___ • 4, 8, 12, 16, 20, ____ • 4, 5, 7, 10, _____, _____

  11. Dilations A dilation is a transformation that changes the size but not the shape of an object or figure. Every dilation has a fixed point that is called the center of dilation.

  12. Dilations To dilate an object: 1) Graph object if necessary. 2) Multiply the coordinates of the object by the scale factor. 3) Graph new coordinates.

  13. Dilations Example 1:

  14. Dilations

  15. Dilations

  16. Dilations

  17. Dilations Your turn:

  18. Dilations Your turn:

  19. Homework • Page 582 14 - 18 • Page 588 14 – 16 • Page 597 12 – 15

  20. Ex. 2: Comparing Similar Polygons • If XYZW ~ QRSP by a scale factor of 2:1; what is a? a

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