1. 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

2. 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.

3. Lets label the congruent parts L NM P Q R  N  R  L  P  M  Q NL  RP LM  PQ NM  RQ  NLM   RPQ

4. There is a theorem. If two angles of one triangle are congruent to two angles of another triangle, then the third angle is congruent

5. If three sides of a triangle are congruent to three sides of another triangle, then the triangles are congruent. Lets look at some postulates Side Side Side (SSS) Postulate A B C D E F ABCDEF

6. 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. Just one more postulate Side Angle Side (SAS) Postulate A B C D E F ABCDEF

7. Are the following congruent ? Yes SSSSAS No It’s the wrong angle No One angle is off

8. Now, its time for a proof. Given: HFHJ, FGJI, H is midpoint of GI. Prove: FGHJIH StatementReason 1. Given1. HF  HJ, FG  JI H is midpont of GI 2. Def. of midpoint 2. GH  HI 3.  FGH  JIH 3. SSS HG FJ I

9. Given: EBCB, ABDB Prove: AEBDCB Last proof. StatementReason 1. Given1. EB  CB, AB  DB 2. Vertical  ’s 2.  EBA  CBD 3.  AEB  DCB 3. SAS B E A D C