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