Triangle Inequalities

Learn and apply triangle inequalities.

Lesson 4 of 53 parts Practice Flashcards

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Triangle Inequality

Objective: Apply triangle inequality in triangle problems.

For a triangle with sides a,b,c, each side is less than the sum of the other two.

Worked examples

Try itCould lengths 4, 5, and 22 make a triangle?Show answer

No. The sum of the first two is less than the third; triangle inequality fails.

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Objective: Apply triangle inequality in triangle problems.

For a triangle with sides a,b,c, each side is less than the sum of the other two.

Worked examples

Try itCould lengths 4, 5, and 22 make a triangle?Show answer

No. The sum of the first two is less than the third; triangle inequality fails.

Objective: Apply possible third side in triangle problems.

For sides a,b, a third side x must satisfy |a−b|<x<a+b.

Worked examples

Try itFor sides 6 and 9, which could be the integer third side?Show answer

8. The third side must be greater than 3 and less than 15; 8 qualifies.

Objective: Apply side-angle relationships in triangle problems.

In a triangle, the longest side lies opposite the largest angle.

Worked examples

Try itTriangle T1 has side lengths 3, 6, 8. Which side is opposite its largest angle?Show answer

8. The largest angle is opposite the longest side.

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