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Proving Triangles Congruent

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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Proving Triangles Congruent

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  1. Proving Triangles Congruent

  2. 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

  3. SSS Postulate: If the sides of one triangle are congruent to the corresponding sides of a second triangle, then the triangles are congruent.

  4. Given: GH bisects LR at H G Ex. L R H Conclusion:GLH  GRH by SSS Postulate

  5. 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.

  6. Given : T is the midpoint of RI B S I R T Conclusion:SIT   BRT by SAS Postulate

  7. 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.

  8. T D 2 1 4 3 P A Conclusion:DAP  ADT by ASA Postulate

  9. 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.

  10. Correspondences that does not guarantee CONGRUENCE ASS AAA

  11. AAA Correspondence 60° 60° 60°

  12. ASS Correspondence AMBIGUOUS Correspondence

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