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**Proving Triangles Congruent**

SSS Postulate, SAS Postulate ASA Postulate, AAS Theorem & HL Theorem

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**Side - Side - Side Postulate**

C B If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. ABC DEF F E D

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SSS Example: E T I K ITK ETK

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**Side - Angle - Side Postulate**

J L K If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the two triangles are JKL MNO O N M

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SAS Example ARK ? K N E R A ERN

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**Angle - Side - Angle Postulate**

R Q P If two angles and the included side of one triangle are to two angles and the included side of another triangle, then the triangles are PQR STU U T S

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ASA Example YMA ? M Y R A YRA AY Bisects < MAR

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**Angle - Angle - Side Theorem**

Z Y X If two angles and a nonincluded side of one triangle are to two angles and the corresponding nonincluded side, then the triangles are XYZ JAC C J A

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AAS Example K Y R E RKY ? KRE

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**Hypotenuse-Leg Theorem**

If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are RPW SBM R W P M B S

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HL Example Q QMC ? M QHC H C

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Example 1 M E K I IEM ? IEK Property? SAS

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Example 2 RBA ? T I B A IBT Property? R ASA

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**MOU ? None Property? Example 3 None: SSA isn’t a property O U S M**

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Example 4 RIK ? K S I R SKI Property? SSS

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Example 5 SIL ? L A S I LAS Property? AAS

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Example 6 RBI ? R B G GBI Property? HL I

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MISSING PARTS What information do you need to prove the following triangles are congruent by SAS? Q E W T R

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MISSING PARTS What information do you need to prove the following triangles are congruent by ASA? D F 63o G 63o A S

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MISSING PARTS What information do you need to prove the following triangles are congruent by AAS? Y T I U

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MISSING PARTS What information do you need to prove the following triangles are congruent by SSS? Y 6 B C 6 V

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MISSING PARTS What information do you need to prove the following triangles are congruent by HL? Q M H C

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

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

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