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8.3 Similar Polygons

8.3 Similar Polygons. Warmup - Simplify. Identifying Similar Polygons. Definition: Similar Polygons T wo polygons such that their corresponding angles are congruent and the lengths of corresponding sides are proportional the two polygons. Similar polygons. If ABCD ~ EFGH, then. G. H.

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8.3 Similar Polygons

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  1. 8.3 Similar Polygons

  2. Warmup - Simplify

  3. Identifying Similar Polygons Definition: Similar Polygons • Two polygons such that their corresponding angles are congruent and the lengths of corresponding sides are proportional the two polygons.

  4. Similar polygons • If ABCD ~ EFGH, then G H C D F B A E

  5. Similar polygons • Given ABCD ~ EFGH, solve for x. G H C D 6 x B F 2 4 A E 2x = 24 x = 12

  6. Is ABC ~ DEF? Explain. B D 6 E 13 12 5 7 A C F 10 ABC is not similar to DEF since corresponding sides are not proportional. ? ? yes no

  7. Similar polygons Given ABCD ~ EFGH, solve for the variables. G H C D 5 x B F 10 2 y 6 A E

  8. If two polygons are similar, then the ratio of the lengths of two corresponding sides is called the scale factor. Ex: Scale factor of this triangle is 1:2 9 4.5 3 6

  9. Quadrilateral JKLM is similar to PQRS. Find the value of z. R K L S 15 Q z 6 P J M 10 15z = 60 z = 4

  10. Theorem • If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths. • If KLMN ~ PQRS, then

  11. Given ABC ~ DEF, find the scale factor of ABC to DEF and find the perimeter of each polygon. E P = 8 + 12 + 20 = 40 B P = 4 + 6 + 10 = 20 12 20 10 6 A C D F 8 4 CORRESPONDING SIDES 4 : 8 1 : 2

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