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Similarity Tests for Triangles

Similarity Tests for Triangles. S. Angle Angle Similarity Postulate ( AA~). Y. X. Z. R. T. Therefore,  XYZ ~ RST by AA~. P. Side-Side-Side Similarity Theorem ( SSS~). W. Put the three sides from one triangle in order on top. 14. 4. 10.5. 3.

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Similarity Tests for Triangles

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  1. Similarity Tests for Triangles

  2. S Angle Angle SimilarityPostulate ( AA~) Y X Z R T Therefore,  XYZ ~ RST by AA~

  3. P Side-Side-Side SimilarityTheorem ( SSS~) W Put the three sides from one triangle in order on top. 14 4 10.5 3 Put the three sides from the other triangle in order on bottom. X 12 V R 16 Q Therefore,  WXV ~ PRQ by SSS~ Divide out each ratio and see if all three are the same. If so, the triangles are similar.

  4. First, make sure you have a pair of corresponding angles congruent. P Side-Angle-Side SimilarityTheorem ( SAS~) W Put the two sides from one triangle that form that angle in order on top. 4 3 X 12 V R 16 Q Put the two sides from the other triangle forming the angle in order on bottom. Divide out each ratio and see if both are the same. If so, the triangles are similar. Therefore,  WXV ~ PRQ by SAS~

  5. What parts do you know? Test for SSS~. E xamples 6 15 18 Yes! KML ~QSR by SSS~ 10 25 30 = .6 = .6 .6

  6. 1st, write given info on the figure. Now, What do you know? You know vertical angles are congruent, so mark them. Next, you know the two sides that form the angles….check for SAS! AC + CD = AD 6 + CD = 10 CD = 4 E xamples 6 BC + CE = BE 9 + CE = 15 CE = 6 4 4 6 Yes! DCE ~ACB by SAS~ 6 9 .6rep = .6rep

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