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Triangle Similarity

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**Two Triangles are similar if :**

AA ~ : two pairs of corresponding angles are congruent, SSS~ : all three pairs of corresponding sides are proportional, or SAS~ : two pairs of corresponding sides are proportional and their included angles are congruent.

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AA ~ If 2 corresponding angles are congruent then the 3rd pair of corresponding angles must be congruent also. (Angle sum of a triangle = 180°.) A 65° 49° A’ 65° 49°

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**SSS~ = = AB BC AC A’B’ B’C’ A’C’**

You should be able to identify a scale factor. = = A B C 15 9 12 A’ = 7.5 4.5 B’ C’ Scale factor is 2 to 1 or 1/2 6

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SAS~ The included angles are the angles that are formed by the two pairs of corresponding sides. A 65° C 9 12 A’ 4.5 65° C’ 6

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**A Postulate is a statement that is accepted to be true without PROOF.**

POSTULATES AA~ SSS~ SAS~ A Postulate is a statement that is accepted to be true without PROOF.

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**What did you discover with your triangle cutting exercise?**

(cut parallel to C’T’) T C A Do NOT cut this original Triangle. A’ C’ T’ T’’’ C’’’ A’’’ A’’ C’’ T’’

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**Hopefully… Corresponding angles are @**

Corresponding sides are proportional Regardless of where you make your cut.

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**Side-Splitting Theorem**

A line parallel to one side of a triangle divides the other two sides proportionally. 4 3 8 10 2/3

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**How many ratios do you see?**

4 3 8 10 2/3

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**How many ratios do you see?**

4 3 8 10 2/3 / /3 = =

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