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7 4 Similar Triangles and t-5

Geometry similar triangles

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7 4 Similar Triangles and t-5

  1. 1. 7-4 A Postulate for Similar Triangles 7-5 Theorems for Similar Triangles Chapter 7 Ratio, Proportion and Similarity Objective: I can use the AA Similarity Postulate, SAS Similarity Theorem and the SSS Similarity Theorem to prove triangles similar.
  2. 2. Postulate 15 AA Similarity If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
  3. 3. Theorem 7-1 SAS Similarity Theorem  If an angle of one triangle is congruent to an angle of another triangle and the sides including those angles are in proportion, then the triangles are similar. 6 12 18 Since ∠𝐶 ≅ ∠𝐶 and 6 9 = 10 15 , ∆𝐷𝐶𝐸~∆𝐴𝐶𝐵
  4. 4. Theorem 7-2 SSS Similarity Theorem If the sides of two triangles are in proportion, then the triangles are similar. Since 3 6 = 5 10 = 6 12 , ∆𝐾𝐿𝑀~∆𝐾𝑂𝑁
  5. 5. Example 1  Determine if the triangles are similar. If so, tell why and write the similarity statement and similarity ratio.
  6. 6. Answers  Similar : Yes  Why:SSS Similarity  Similarity Statement:∆𝑃𝑄𝑅~∆𝑃𝑅𝑆  Similarity Ratio: 2 to 3
  7. 7. Example 2  Determine if the triangles are similar. If so, tell why and write the similarity statement and similarity ratio.
  8. 8. Answers  Similar : Yes  Why: AA Similarity  Similarity Statement:∆𝐶𝐵𝐴~∆𝐻𝐺𝐹  Similarity Ratio: none

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