5.3 Proving Triangles Congurent using SAS

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Presentation transcript:

5.3 Proving Triangles Congurent using SAS

What we will learn Prove triangles congruent using side angle side theorem Using diagrams

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

Ex. 1 and 2 Proving Triangles Congruent Statement Reason 1. 1. Given 2. 𝐴𝐶 ≅ 𝐴𝐶 2. Reflex. Prop. 3. ∠𝐵𝐶𝐴≅∠𝐷𝐴𝐶 3. Alt. Int. Angles 4. △𝐴𝐵𝐶≅△𝐶𝐷𝐴 4. SAS

Your Practice Statement Reason 1. B is the midpoint of 𝐴𝐷 . ∠𝐴𝐵𝐶 𝑎𝑛𝑑∠𝐷𝐵𝐶 are right angles. 1. Given 2. ∠𝐴𝐵𝐶≅∠𝐷𝐵𝐶 2. Right Angles ≅ Thm 3. 𝐴𝐵 ≅ 𝐷𝐵 3. Def of Midpt 4. 𝐵𝐶 ≅ 𝐵𝐶 4. Reflex. Prop. 5. △ABC≅△𝐷𝐵𝐶 5. SAS