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1/23/15 Unit 7

Congruency and Similarity

(AA, SSS, SAS)

Proving Triangles Similar

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AA Similarity (Angle-Angle)

A D

If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar….or the third pair of angles are congruent.

E

DA

B

CF

B EABC ~ DEFConclusion:

andGiven:

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SSS Similarity (Side-Side-Side)If the measures of the corresponding sides of two triangles are in the same ratio, then the triangles are similar.

E

DA

B

CF

Given:

Conclusion:

5

11 22

8 1610

BC

EF

AB

DEAC

DF

8

16

5

10

11

22

ABC ~ DEF

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SAS Similarity (Side-Angle-Side)

ABC ~ DEF

If the measures of two sides of a triangle are in the same ratio to the measures of two corresponding sides of another triangle and the angles between them are congruent, then the triangles are similar.

Given:

Conclusion:

E

DA

B

CF

5

11 22

10

AB ACA D and

DE DF