Similarity Tests for Triangles Angle Angle Similarity Postulate ( AA~) X Y Z RT S Therefore,  XYZ ~  RST by AA~

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Presentation transcript:

Similarity Tests for Triangles

Angle Angle Similarity Postulate ( AA~) X Y Z RT S Therefore,  XYZ ~  RST by AA~

Congruent Angles????? Vertical Angles Theorem Vertical Angles Theorem Right Angles Congruence Theorem Right Angles Congruence Theorem

Congruent Angles????? Corresponding Angles Postulate Corresponding Angles Postulate Reflexive Property (shared angle) Reflexive Property (shared angle)

Congruent Angles????? Alternate Interior Angles Theorem Alternate Interior Angles Theorem

Congruent Angles????? Alternate Exterior Angles Theorem Alternate Exterior Angles Theorem

Congruent Angles????? Don’t forget Triangle Sum Theorem to find missing angles Don’t forget Triangle Sum Theorem to find missing angles = – 105 = o

Side-Side-Side Similarity Theorem ( SSS~) X W V RQ P Therefore,  WXV ~  PRQ by SSS~ Put the three sides from the other triangle in order on bottom. Put the three sides from one triangle in order on top. Divide out each ratio and see if all three are the same. If so, the triangles are similar.

Side-Angle-Side Similarity Theorem ( SAS~) X W V RQ P Therefore,  WXV ~  PRQ by SAS~ 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. First, make sure you have a pair of corresponding angles congruent. Put the two sides from one triangle that form that angle in order on top.

E xamples What parts do you know? Test for SSS~ /5 = = Yes!  KML ~  QSR by SSS~

E xamples /3 = Yes!  CDE ~  CAB by SAS~ 1 st, write given info on the figure. AC + CD = AD 6 + CD = 10 CD = 4 4 BC + CE = BE 9 + CE = 15 CE = 6 6 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!