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Proving Triangles Congruent. RECALL There are 4 cases in which we can conclude that a correspondence between two triangles is a congruence: SSS (Side-Side-Side) correspondence SAS (Side-Angle-Side) correspondence ASA (Angle-Side-Angle) correspondence SAA (Side-Angle-Angle) correspondence.
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RECALLThere are 4 cases in which we can conclude that a correspondence between two triangles is a congruence: • SSS (Side-Side-Side) correspondence • SAS (Side-Angle-Side) correspondence • ASA (Angle-Side-Angle) correspondence • SAA (Side-Angle-Angle) correspondence
SSS Postulate: If the sides of one triangle are congruent to the corresponding sides of a second triangle, then the triangles are congruent.
Given: GH bisects LR at H G Ex. L R H Conclusion:GLH GRH by SSS Postulate
SAS Postulate: If two sides and their included angle of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.
Given : T is the midpoint of RI B S I R T Conclusion:SIT BRT by SAS Postulate
ASA Postulate: If two angles and their included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.
T D 2 1 4 3 P A Conclusion:DAP ADT by ASA Postulate
Can you state the AAS Theorem? AAS Theorem: If two sides and their non-included angle of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.
AAA Correspondence 60° 60° 60°
ASS Correspondence AMBIGUOUS Correspondence