3.2 Three Ways to Prove a Triangle Congruent Kaylee Nelson Period: 8

Included Angles and Included Sides An included angle is an angle made by two lines with a common vertex An included side is a side that links two angles together

Three Ways to Prove Triangles Congruent Angle-Side-Angle (ASA) Side-Side-Side (SSS) Side-Angle-Side (SAS)

The Angle – Side – Angle Postulate The Angle – Side - Angle postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then these two triangles are congruent.

Sample Problem (ASA) Since angle A is congruent to angle X, segment AB is congruent to segment XY, and angle B is congruent to angle Y, the triangles are congruent through ASA.

The Side – Side – Side Postulate The Side – Side - Side postulate states that if three sides of one triangle are congruent to three sides of another triangle, then these two triangles are congruent.

Sample Problem (SSS) Since segment ZX is congruent to segment CA, segment XY is congruent to segment AB, and segment YZ is congruent to segment BC, the triangles are congruent through SSS

The Side – Angle – Side Postulate The Side - Angle - Side postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.

Sample Problem (SAS) Since segment AC is congruent to segment ZX, angle ACB is congruent to angle XZY, and segment CB is congruent to segment ZY, the triangles are congruent through SAS

Practice Problem One

Practice Problem Two

Practice Problem Three

Answer Key

Practice Problem One

Practice Problem Two

Practice Problem Three

Works Cited Morris, Vernon. "Proving Congruent Triangles." Math Warehouse. 28 May Page, John. Math Open Reference May Rhoad, Richard, George Milauskas, Robert Whipple. Geometry for Enjoyment and Challenge. Evanston, Illinois: McDougal, Littell & Company, 1991.