Proving triangles are congruent: sss and sas

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Presentation transcript:

Proving triangles are congruent: sss and sas Big idea: reasoning and proof Essential understandings: Two triangles can be proven to be congruent without having to show that all corresponding parts are congruent Two ways triangles can be proven to be congruent are by using three pairs of corresponding sides or by using two pairs of corresponding sides and one pair of corresponding angles. Mathematical practice: Look for and make use of structure

Math background In the last lesson, you learned that if all six pairs of corresponding sides and angles are congruent, then the triangles are congruent. In this lesson and the next, you will learn that you do not need all six of the pieces of information above to prove that the triangles are congruent. The SSS and SAS Postulates allow you to prove two triangles are congruent by showing only three conditions are true. Students will learn that S stands for side and A stands for angle in the triangle.

Congruence postulates SIDE-SIDE-SIDE (SSS) CONGRUENCE POSTULATE: If _______________ sides of one triangle are _______________ to three _______________ of a second triangle, then the two _______________ are congruent SIDE-ANGLE-SIDE (SAS) CONGRUENCE POSTULATE: If _______________ sides and the _______________ angle of one triangle are _______________ to two _______________ and the included _______________ of a second triangle, then the two _______________ are congruent.

EX: Decide whether enough information is given to prove that the triangles are congruent. If there is enough information, state the congruence postulate you would use. 1. 2.

EX: Decide whether enough information is given to prove that the triangles are congruent. If there is enough information, state the congruence postulate you would use. 3. 4.

EX: Decide whether enough information is given to prove that the triangles are congruent. If there is enough information, state the congruence postulate you would use. 5. 6.

Ex 7: Given: Prove: STATEMENTS REASONS

EX 8: GIVEN: PROVE: STATEMENTS REASONS

EX 9: PROVE THAT