4-3 Triangle Congruence by ASA and AAS
Objective
To prove two triangles congruent using the ASA Postulate and the AAS Theorem
You already know that triangles are congruent if two pairs of sides and the included angles are congruent (SAS). You can also prove triangles congruent using other groupings of angles and sides.
Essential Understanding You can prove that two triangles are congruent without having to show that all corresponding parts are congruent. In this lesson, you will prove triangles congruent by using one pair of corresponding sides and two pairs of corresponding angles.
Take note Postulate 4-3: Angle-Side-Angle (ASA) Postulate
Postulate
If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
If…
Then…
Table of Contents
- 6-1 The Polygon Angle-Sum Theorems
- 6-2 Properties of Parallelograms
- 6-3 Proving That a Quadrilateral Is a Parallelogram
- 6-4 Properties of Rhombuses, Rectangles, and Squares
- 6-5 Conditions for Rhombuses, Rectangles, and Squares
- 6-6 Trapezoids and Kites
- 6-7 Polygons in the Coordinate Plane
- 6-8 and 6-9 Coordinate Geometry and Coordinate Proofs