Triangle Inequalities

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The positions of the longest and shortest sides of a triangle are related to the positions of the largest and smallest angles.

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Presentation transcript:

Triangle Inequalities

Objective I CAN discover the Triangle Inequality Theorem and apply inequalities in one triangle.

The DHS Chick-Fil-A Run The DHS Football team is headed to M&T Bank stadium for the state playoffs. The game isn’t until 7 PM, so they decide to stop for Chick-Fil-A on the way there. A few players don’t want to stop, and head straight for the stadium. Which of the following is a possible distance from DHS to M&T Bank Stadium? 25 6 12 18 20 16 10 miles 6 miles x

Triangle Sides If one side of a triangle is longer than another side, then the angle opposite the longer side has a greater measure than the angle opposite the shorter side.

Examples List the Angles from largest to smallest

Triangle Angles If one angle of a triangle has a greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle.

Examples List the sides of triangle from largest to smallest

Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Example Do these numbers represent a triangle? 1.) 9, 7, 12 2.) 5, 5, 10 3.) 1, 4, 6 4.) 6, 6, 2

Finding Range of Third Side If you are given two sides of a triangle you can determine the range that the third side must fall in.