5-6 Inequalities in One Triangle
Objective
To use inequalities involving angles and sides of triangles
Dynamic Activity
Triangle Inequalities
In the Solve It, you explored triangles formed by various lengths of board. You may have noticed that changing the angle formed by two sides of the sandbox changes the length of the third side.
Essential Understanding The angles and sides of a triangle have special relationships that involve inequalities.
Take Note Property: Comparison Property of Inequality
If
Proof
Proof of the Comparison Property of Inequality
Given:
Prove:
| Statements | Reasons |
|---|---|
|
1)
|
1) Given |
|
2)
|
2) Addition Property of Inequality |
|
3)
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3) Identity Property of Addition |
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4)
|
4) Given |
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5)
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5) Substitution |
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