5-7 Inequalities in Two Triangles
Objective
To apply inequalities in two triangles
In the Solve It, the hands of the clock and the segment labeled x form a triangle. As the time changes, the shape of the triangle changes, but the lengths of two of its sides do not change.
Essential Understanding In triangles that have two pairs of congruent sides, there is a relationship between the included angles and the third pair of sides.
When you close a door, the angle between the door and the frame (at the hinge) gets smaller. The relationship between the measure of the hinge angle and the length of the opposite side is the basis for the SAS Inequality Theorem, also known as the Hinge Theorem.
Take Note Theorem 5-13: The Hinge Theorem (SAS Inequality Theorem)
Theorem
If two sides of one triangle are congruent to two sides of another triangle, and the included angles are not congruent, then the longer third side is opposite the larger included angle.
If …
Then …
You will prove Theorem 5-13 in Exercise 25.
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