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Transcript

4.2 Triangle Congruence by SSS and SAS You will construct and justify statements about triangles using Side Side Side and Side Angle Side Pardekooper First, we need to look at some things. What makes two items congruent? All the corresponding sides are congruent. All the corresponding angles are congruent. Pardekooper Lets label the congruent parts L P N M Q R N R NL RP L P LM PQ M Q NM RQ NLM RPQ Pardekooper There is a theorem. If two angles of one triangle are congruent to two angles of another triangle, then the third angle is congruent Pardekooper Lets look at some postulates Side Side Side (SSS) Postulate If three sides of a triangle are congruent to three sides of another triangle, then the triangles are congruent. B ABCDEF E A D C F Pardekooper Just one more postulate Side Angle Side (SAS) Postulate If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. ABCDEF B E A Pardekooper D C F Are the following congruent ? No Yes It’s the wrong SAS SSS angle Pardekooper One angle is off Now, its time for a proof. Given: HFHJ, FGJI, H is midpoint of GI. Prove: FGHJIH F G J H I Statement Reason 1. HFHJ, FGJI 1. Given H is midpont of GI 2. GHHI 2. Def. of midpoint 3. FGHJIH 3. SSS Pardekooper Last proof. Given: EBCB, ABDB Prove: AEBDCB E D C B A Statement Reason 1. EBCB, ABDB 1. Given 2. EBACBD 2. Vertical ’s 3. AEBDCB 3. SAS Pardekooper