5-5 Inequalities in Triangles

L.E.Q. How do you use inequalities involving angles and sides of triangles?

If a = b + c and c > 0, then a > b.

Comparison Property of Inequality

The measure of an exterior angle of a triangle is greater than the measure of each of its remote interior angles.

Corollary to the Triangle Exterior Angle Theorem

In the diagram, by the Isosceles Triangle Theorem. Explain why

Example 1: Applying the Corollary.

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

Theorem 5-10: Larger Angle, Longer Side Theorem.

A landscape architect is designing a triangular deck. She wants to place benches in the two larger corners. Which corners have the larger angles?

Example 2: Real-World Connection.

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

Theorem 5-11: Longer Side, Larger Angle Theorem.

In which side is the shortest?

Longest?

Example 3: Using Theorem 5-11.

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Not every set of three segments can form a triangle. The lengths of the segments must be related in a certain way.

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

Theorem 5-12: Triangle Inequality Theorem.

Example 4: Using the Triangle Inequality Theorem.

Can a triangle have sides with the given lengths? Explain.

3 ft, 7 ft, 8 ft 3 cm, 6 cm, 10 cm

A triangle has sides of lengths 8 cm and 10 cm. Describe the lengths possible for the third side.

Example 5: Finding Possible Side Lengths.

Pgs. 276 – 277 #s 2 – 26 Even.

Homework: