Section 11.6 : Inequalities in One Triangle

Learning Targets: Prepares for – G.CO.10

Important Terms and Definitions

Corollary to the Triangle Exterior Angles Theorem: The measure of an exterior angle of a triangle is greater than the measure of each of its remote interior angles.

Theorem: If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side.

Theorem: If two angles of a triangle are not congruent, then the longer side lies opposite the larger angle.

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

(ex 1) Explain why .

(ex 2) Explain why .

(ex 3) List the angles of the triangle in order from smallest to largest.

(ex 4) List the sides of the triangle in order from shortest to longest.

(ex 5) In , , and . List the sides in order from shortest to longest.

Can a triangle have sides with the given lengths?

(ex 6)

(ex 7)

The lengths of two sides of the triangle are given. Describe possible lengths for the third side.

(ex 8)

(ex 9)

(ex 10) Explain why the triangle below is impossible.

Homework – Section 11.6 : Inequalities in One Triangle

In the figures below, explain why .

1. 2.

List the angles of each triangle in order from smallest to largest.

3. 4. 5.

List the sides of each triangle in order from shortest to longest.

6. 7. 8.

Can a triangle have sides with the given lengths?

9. 11. 10. 12.

The lengths of two sides of the triangle are given. Describe possible lengths for the third side.

13. 14. 15.

Determine which segment is shortest in each diagram.

16. 17.