1Geometry Lesson: Congruent Polygons, Triangles, SAS Aim: What are congruent polygons? How do we prove triangles congruent using Side-Angle-Side Postulate?

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How do we prove triangles congruent using Side-Side-Side Postulate?

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Presentation transcript:

1Geometry Lesson: Congruent Polygons, Triangles, SAS Aim: What are congruent polygons? How do we prove triangles congruent using Side-Angle-Side Postulate? Do Now: A B C D Given: Prove: StatementReason 1) 2) 3) 4) 5) Given Def. angle bisector Complements of the same or congruent angles are congruent.

2Geometry Lesson: Congruent Polygons, Triangles, SAS Def: Congruent Polygons Two polygons are congruent if and only if: a)Corresponding angles are congruent. b)Corresponding sides are congruent. A B C D E F G H

3Geometry Lesson: Congruent Polygons, Triangles, SAS Ex: Congruent Polygons 50º 96º 34º A R Q 96º 34º 50º M H B 1) Given the triangles shown: a) Write a congruence statement for the triangles. b) Which angle is congruent to  H? c) Which side is congruent to side AQ?

4Geometry Lesson: Congruent Polygons, Triangles, SAS Postulate: Postulate: Side-Angle-Side Postulate (SAS) If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. Construct an identical triangle using two sides and the included angle. There is only one length for the 3 rd side that will complete the triangle. x Ex: Which pairs of triangles can be proved congruent using S-A-S? 1)2)3)  X X

5Geometry Lesson: Congruent Polygons, Triangles, SAS Ex 1: Proof w/S.A.S. StatementReason 1) 2) 3) 4) 5) Given Def. angle bisector Reflexive Postulate S.A.S. Postulate 12 A B C D Given: Prove:

6Geometry Lesson: Congruent Polygons, Triangles, SAS Ex 2,3,4: Proofs w/S.A.S. A B C D E 2) Given: Prove: A B C D E 3) Given: Prove: 4) Given: Prove: P A B C D x y