4-4 Using Corresponding Parts of Congruent Triangles
Objective
To use triangle congruence and corresponding parts of congruent triangles to prove that parts of two triangles are congruent
With SSS, SAS, ASA, and AAS, you know how to use three congruent parts of two triangles to show that the triangles are congruent. Once you know that two triangles are congruent, you can make conclusions about their other corresponding parts because, by definition, corresponding parts of congruent triangles are congruent.
Essential Understanding If you know two triangles are congruent, then you know that every pair of their corresponding parts is also congruent.
Proof: Problem 1 Proving Parts of Triangles Congruent
Given:
Prove:
Think
In the diagram, which congruent pair is not marked?
The third angles of both triangles are congruent. But there is no AAA congruence rule. So, find a congruent pair of sides.
✓ Got It?
-
Given:
Prove:
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