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

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Presentation transcript:

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

Determine whether the given measures can be lengths of the sides of a triangle. a. 6, 9, 16 b. 14, 16, 27 Example 4-1c Answer: no Answer: yes

Example 4-2b A 4B 9C 12D 16 Answer: D Multiple-Choice Test Item Which measure cannot be XZ?

The Triangle Inequality Theorem 5.12 The perpendicular segment from a point to a line is the shortest segment from the point to the line. Corollary 5.1 The perpendicular segment from a point to a plane is the shortest segment from the point to the plane.

Example 4-3b Prove: AB > AD Given:is an altitude in  ABC.