# Proving Triangles Congruent

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Proving Triangles Congruent
SSS Postulate, SAS Postulate ASA Postulate, AAS Theorem & HL Theorem

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

SSS Example: E T I K ITK    ETK

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

SAS Example ARK   ? K N E R A ERN

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

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

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

AAS Example K Y R E RKY   ? KRE

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

HL Example Q QMC   ? M QHC H C

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

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

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

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

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

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

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

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

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

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

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

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