Indirect Proof and Inequalities in One Triangle

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Presentation transcript:

Indirect Proof and Inequalities in One Triangle Section 6.5

What You Will Learn Write indirect proofs. List sides and angles of a triangle in order by size. Use the Triangle Inequality Theorem to find possible side lengths of triangles.

Writing an Indirect Proof

Example 1: Writing an Indirect Proof

Relating Sides and Angles of a Triangle Example 2: Relating Side Length and Angle Measure

Triangle Larger Angle Theorem

Ordering Angle Measures of a Triangle You are constructing a stage prop that shows a large triangular mountain. The bottom edge of the mountain is about 32 feet long, the left slope is about 24 feet long, and the right slope is about 26 feet long. List the angles of △JKL in order from smallest to largest.

Ordering Side Lengths of a Triangle List the sides of △DEF in order from shortest to longest.

Finding Possible Side Lengths A triangle has one side of length 14 and another side of length 9. Describe the possible lengths of the third side.