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+ 4.2 Triangle Congruence by SSS and SAS Objective: To prove two triangles congruent using the SSS and SAS Postulates + Angle-Side-Angle Postulate ASA If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. + Side-Side-Side Postulate SSS If 3 sides of one triangle are congruent (≅) to 3 sides of another triangle, then the triangles are congruent (≅). ABC DEF Notice the order in which the congruency statement is given + 1.Which other side do we know is congruent? Why? 1.Which two triangles are congruent? 1.How do you know? + Included Angles and Sides + Side-Angle-Side Postulate SAS If 2 sides and the included angle of one triangle are congruent (≅) to 2 sides and the included angle of another triangle, then the 2 triangles are congruent (≅) . ABC DEF Notice the order in which the congruency statement is given + Practice Name the triangle congruence postulate, if any, that you can use to prove each pair of triangles congruent. Then, write a congruence statement. 1. 2. 3. + Practice From the information given, can you prove AEB CDB ? + Tips Mark any given information on your diagram. Look to see if your triangles “share” parts. These common parts are automatically one set of congruent parts. If not given all the pieces you need to prove the triangles congruent, look to see what else you might know about the diagram. (For example: vertical angles, shared sides, etc.) + Methods that DO NOT Prove Triangles to be Congruent + Methods that DO NOT Prove Triangles to be Congruent