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Transcript
Geometry – 4.4 Proving Triangles Congruent – SSS , SAS Postulate 4.1 - SSS Postulate If __________ sides of one triangle are __________________ to ____________ sides of a _______________ triangle, then the triangles are _______________. Side 𝐴𝐵 ≅ _________ Side 𝐵𝐶 ≅ _________ Side 𝐴𝐶 ≅ _________ Then ∆𝐴𝐵𝐶 ≅ ___________ Included Angle: Postulate 4.2 – SAS Postulate If____________ sides and the _________________ angle of one triangle are __________________ to ___________ sides and the ___________________ angle of a second triangle, then the triangles are ___________________. Side 𝐴𝐵 ≅ ____________ Angle ∠𝐵 ≅ ___________ Side 𝐵𝐶 ≅ ____________ Then ∆𝐴𝐵𝐶 ≅ _______________ Geometry – 4.4 Proving Triangles Congruent – SSS , SAS Example 1: Identify Congruent Triangles Determine which postulate can be used to prove that the triangles are congruent. Also, name the congruent sides and angles if any. a. b. c. d. e. f. Geometry – 4.4 Proving Triangles Congruent – SSS , SAS Example 2: SSS on a Coordinate Plane a. Triangle ABC has vertices A(1, 1), B(0, 3), and C(2, 5). Triangle EFG has vertices E(1, -1), F(2, -5) and G(4, -4). Determine if the triangles are congruent. b. Triangle JKL has vertices J(2, 5), K(1,1), and L(5,2). Triangle NPQ has vertices N(-3,0), P(-7,1) and Q(-4.4). Determine if the triangles are congruent.