Proving Triangles are Congruent SSS and SAS Chapter 4.4 Video 2:21-7:42.

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Presentation transcript:

Proving Triangles are Congruent SSS and SAS Chapter 4.4 Video 2:21-7:42

SSS   Theorem If all three sides of one triangle, are congruent to the corresponding sides in a second triangle, then the triangles are congruent.

SSS   Theorem B C A X Z Y  ABC   XYZ

Write a two column proof: Given: AB AC and BX CX Prove:  BXA   CXA Given 2. Reflexive Property 3. SSS   Thm 1. A C B X 2.2.

B. Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible. Each pair of corresponding sides are congruent. Two are given and the third is congruent by Reflexive Property. So the triangles are congruent by SSS. Answer: SSS

reflexive Reasons Proof: Statements 3. SSS 3. ΔABG ΔCBG 1. Given _________ 2.

SAS   Theorem If two sides and the included angle of one triangle, are congruent to the corresponding sides and angle in a second triangle, then the triangles are congruent.

SAS   Theorem B C A X Z Y  ABC   XYZ

Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible. Two sides and the included angle of one triangle are congruent to two sides and the included angle of the other triangle. The triangles are congruent by SAS. Answer: SAS

1.A 2.B 3.C A.SSS B.SAS C.not possible Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible.

1.A 2.B 3.C A.SSS B.SAS C.not possible Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible.

Homework Chapter 4-4 Pg all 9, all all