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Wednesday, September 25 th

Wednesday, September 25 th. Warm Up. S is the centroid. If MS=12, what is SP? If NQ=18, what is SQ?. Today’s Goal. Identify similar polygons. Apply properties of similar polygons to solve problems. Which shapes are similar and how do you know?. 1. 3. 2.

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Wednesday, September 25 th

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  1. Wednesday, September 25th Warm Up S is the centroid. If MS=12, what is SP? If NQ=18, what is SQ?

  2. Today’s Goal Identify similar polygons. Apply properties of similar polygons to solve problems.

  3. Which shapes are similar and how do you know? 1. 3. 2.

  4. Figures that are similar(~) have the same shape but not necessarily the same size.

  5. Remember-Congruent Represented by: Have the same size and shape EXACTALY THE SAME!!!!!

  6. Two polygons are similar polygons if and only if their corresponding angles are congruent and their corresponding side lengths are proportional. Definition

  7. Similar figures have the same shape but not necessarily the same size.

  8. Finding missing angles What is angle D? <D • Hint: Remember angles are the same in corresponding angles!

  9. #1 Identify the pairs of congruent angles and corresponding sides 0.5 N  Q and P  R. By the Third Angles Theorem, M  T.

  10. #2 Identify the pairs of congruent angles and corresponding sides B  G and C  H. By the Third Angles Theorem, A  J.

  11. A similarity ratiois the ratio of the lengths of the corresponding sides of two similar polygons. The similarity ratio of ∆ABC to ∆DEF is , or . The similarity ratio of ∆DEF to ∆ABC is , or 2.

  12. Think: What am I multiplying or dividing all sides by to get the lengths of the other triangle? Also known as the SCALE FACTOR or DIALATION

  13. Writing Math Writing a similarity statement is like writing a congruence statement—be sure to list corresponding vertices in the same order.

  14. #1 Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement. ∆ABCD and ∆EFGH

  15. Step 1 Identify pairs of congruent angles. P  R and S  W isos. ∆ Step 2 Compare corresponding angles. mW = mS = 62° mT = 180° – 2(62°) = 56° Since no pairs of angles are congruent, the triangles are not similar.

  16. #2 Determine if ∆JLM ~∆NPS. If so, write the similarity ratio and a similarity statement. Step 1 Identify pairs of congruent angles. N  M, L  P, S  J

  17. Thus the similarity ratio is , and ∆LMJ ~ ∆PNS. Step 2 Compare corresponding sides.

  18. Finding Scale Factor Practice

  19. Ticket to Go: Textbook page 249 1-20

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