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Geometry Triangle Congruence by SSS and SAS Notes Date: _____ Objective: To prove two triangles congruent using the SSS and SAS Postulates In section 4-1 you learned that if two triangles have three pairs of congruent corresponding angles and three pairs of congruent corresponding sides, then the triangles are congruent. If you know this: A X B Y AB XY C Z BC YZ AC XZ Then you know this: ________ ________ However, you do not need to know that all _____ corresponding parts are ______________ in order to conclude that two triangles are _____________. We have 5 ‘shortcuts’ that we will learn the rest of this unit that can help us prove that 2 triangles are congruent. This section introduces the first 2 shortcuts. Side-Side-Side Postulate (SSS) If three sides of one triangle are congruent to the three sides of another triangle, then Example 1: The bridge girders are the same size, as marked. Explain why ABD CBD. Example 2: Example 3: The triangles below are congruent by SSS. Write a congruence statement. Side-Angle-Side Postulate (SAS) If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then *The word _________________ is used frequently when referring to the angles and sides of a triangle. Draw BNX below. BX is included between ____ and ______. N is included between ____ and ______. Example 4: The triangles below are congruent by SAS. Write a congruence statement. Example 5: Given: P is the midpoint of AE and BK . Prove: ABP EKP . (The “trick” to these kind of triangle proofs is you will always have enough information to get 3 congruent parts to use a shortcut.) Statements P is the midpoint of AE Justifications Definition of midpoint P is the midpoint of BK ABP EKP Example 6: RS TK . What other information do you need to prove RSK TKS by SAS? Example 7: What other information do you need to prove ABC CDA by SAS? Example 8: From the information given, can you prove the two triangles congruent? If so, state the postulate that proves them congruent. If not, explain why. A) RED CAT B) AEB DBC C) D is the midpoint of AB .