the triangle inequality triangle inequality theorem the sum of the lengths of any two sides of a...

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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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

Answer: no

Answer: yes

Page 3: 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

A 4 B 9 C 12 D 16

Answer: D

Multiple-Choice Test ItemWhich 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.

Page 5: 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

Prove: AB > AD

Given: is an altitude in ABC.

TRIANGLE INEQUALITY THEOREM

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