Take note Postulate 4-1: Side-Side-Side (SSS) Postulate
Postulate
If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.
If…
Then…
As described in Chapter 1, a postulate is an accepted statement of fact. The Side-Side-Side Postulate is perhaps the most logical fact about triangles. It agrees with the notion that triangles are rigid figures; their shape does not change until pressure on their sides forces them to break. This rigidity property is important to architects and engineers when they build things such as bicycle frames and steel bridges.
Proof: Problem 1 Using SSS
Plan
You have two pairs of congruent sides. What else do you need?
You need a third pair of congruent corresponding sides. Notice that the triangles share a common side,
Given:
Prove:
✓ 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