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Triangle Inequalities

Activity Overview

In this activity, students will discover the Triangle Inequality Theorem and explore the possible lengths of the third side of a triangle given the other two side lengths. Students will also classify the type of triangle as acute, obtuse, or right using the Pythagorean inequalities.

Key Steps

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    In this activity, students will begin by looking at a triangle and investigating the possible lengths of the third side given the other two sides.

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    Next, students will investigate a given triangle and the lengths of all of its sides. Students will be asked to move a point on the triangle to determine for what type of triangle exists when a2 + b2 = c2, a2 + b2 > c2, and a2 + b2 < c2.

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    Finally, students will apply what they have learned to answer questions about the inequalities they explored.

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