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Proof Options: The base angles of an isosceles triangle are congruent. A B C D Basic Paragraph Proof: Since the largest side of a triangle is across from the largest angle, the smallest side is across from the smallest side, it seem reasonable that if two sides were of equal length the angles across from them, which are the base angles of an isosceles triangle, would also be equal in measure. Alternate Paragraph Proof: If you drop an altitude to the base of the non-congruent side, it is a line of symmetry. It creates two, symmetric, congruent triangles that have corresponding angles at ends of the non-congruent sides. These angles, which are the base angles of the isosceles triangle, are congruent as corresponding parts of congruent triangles. Two-Column Proof: Given AB @ AC . Prove Statements 1. AB @ AC 2. AD bisects ÐBAC 3. ÐABC @ ÐACB 4. AD @ AD 5. DABD @ DACD 6. ÐABD @ ÐACD ÐABD @ ÐACD Reasons 1. Given 2. Construction of the Angle Bisector 3. Definition of Angle Bisector 4. Reflexive Property 5. SAS congruence 6. Corresponding Parts of Congruent Triangles are Congruent All ProofBlock resources have been adapted with permission from Jennifer and Nathaniel Dirksen, creators of ProofBlocks. To access additional ProofBlock resources, visit http://www.proofblocks.com Proof Blocks: AB @ AC Construction of the Angle Bisector (Blank Block) AD bisects ÐBAC ÐABC @ ÐACB AD @ AD DABD @ DACD ÐABD @ ÐACD