Triangle Congruence by SSS and SAS Learning Target: I can prove two triangles congruent using the SSS and SAS Postulate.

Side-Side-Side Postulate (SSS Postulate) If three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent. Q H P G R F What can we conclude about the triangles using SSS Postulate? Triangle GHF is congruent to Triangle PQR

Decide with your partner which can be proven with SSS. If not, what information is missing? 1. Pink can be proven with SSS 2. Green can be proven with SSS 3. Yellow can be proven with SSS 4. Blue cannot be proven with SSS because we need the other pair of sides.

Given: AB≅CB, AD≅CD B Prove: ABD≅ CBD A C D Statements Reasons AB≅CB Given AD≅CD Given BD≅BD Reflexive Property Triangle ABD is SSS Postulate congruent to Triangle CBD A C D

Side-Angle-Side Postulate (SAS Postulate) If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. ***In this case, included means between the two sides*** B F C A D E What can we conclude about the triangles using SAS Postulate? Triangle BCA is congruent to Triangle FDE

Decide with your partner which can be proven with SAS. If not, what information is missing? 1. Pink cannot be proven with SAS because the angle is not in between the two sides. 2. Green can be proven. 3. Yellow can be proven. 4. Blue can be proven.

Given: AB≅BD, EB≅BC Prove: ABE≅ DBC A B C E D Statements Reasons AB≅BD Given EB≅BC Given <ABE≅<DBC Vertical angles are congruent Triangle ABE is SAS Postulate congruent to Triangle DBC D