Triangle Inequalities Objectives: 1.Discover inequalities among sides and angles in triangles.

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Triangle Inequalities

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Presentation transcript:

Triangle Inequalities Objectives: 1.Discover inequalities among sides and angles in triangles.

Triangle Inequality Conj. The sum of the lengths of the shorter two sides of a triangle is ___________ the length of the third side. greater than

Is it possible to have a triangle with the following side measures?

Side-Angle Inequality Conj In a triangle, the longest side is opposite the angle with greatest measure, and the shortest side is opposite the angle with the least measure.

List the sides in order from shortest to longest.

List the angles in order from smallest to greatest measure.

Definitions:

If you extend one side of a triangle from the vertex, you form an exterior angle. exterior angle

The angle adjacent to the exterior angle. adjacent interior angle

The two angles that are non- adjacent to the exterior angle. remote interior angles

Triangle Exterior Angle Conjecture: The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.

What does Triangle Exterior angle Conjecture mean? m  A = m  B + m  C

m  A=120° m  A= ?

m  B=138° m  B= ?

m  C=83° m  C= ?