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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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Congruent Triangles have six sets of corresponding parts! Three sets of corresponding sides Three sets of corresponding angles.

Congruent Triangles have six sets of corresponding parts! Three sets of corresponding sides Three sets of corresponding angles.

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