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Objectives

Objectives. Prove that two triangles are similar using AA, SAS, and SSS. Proving Two Triangles Similar with Shortcuts.

jillian-adriano
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Objectives

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  1. Objectives • Prove that two triangles are similar using AA, SAS, and SSS

  2. Proving Two Triangles Similar with Shortcuts • Instead of using the definition of similarity to prove that two triangles are congruent (all corresponding angles are congruent and all corresponding sides are proportional), you can use three shortcuts: • Angle-Angle (AA) • Side-Angle-Side (SAS) • Side-Side-Side (SSS)

  3. Angle-Angle (AA) Similarity Postulate • If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

  4. AA Example Explain why the triangles are similar and write a similarity statement. ∠R ≅ ∠V (Given) ∠RSW ≅ ∠VSB (vertical angles are congruent) ΔRSW ≅ ΔVSB (AA)

  5. Side-Angle-Side (SAS) Similarity Theorem • If an angle of one triangle is congruent to an angle of a second triangle and the sides including the two angles are proportional, then the triangles are similar. G A 2 4 B C 3 J 6 H ΔABC ~ ΔGJH

  6. SAS Example Explain why the two triangles are similar and write a similarity statement. ∠Q ≅ ∠X since they are right angles The two sides that include the right angles are proportional By SAS, ΔPRQ ~ΔZYX

  7. Side-Side-Side (SSS) Similarity Theorem • If the corresponding sides of two triangles are proportional, then the triangles are similar. G A 4 5 8 10 B C 6 J 12 H ΔABC ~ ΔGJH

  8. SSS Example Explain why the two triangles are similar and write the similarity statement. Since all sides of the two triangles are proportional, by SSS, ΔABC ~ ΔEFG

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