Triangle Theorems.

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Presentation transcript:

Triangle Theorems

the sum of the measures of the interior angles of a triangle is 180 . Triangle Sum Theorem: the sum of the measures of the interior angles of a triangle is 180 .

Remote Interior Angles of a Triangle: the two angles that are non-adjacent to the specified exterior angle

Exterior Angle Theorem: the measure of the exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

Exterior Angle Inequality Theorem: the measure of an exterior angle of a triangle is greater than either of the remote interior angles.

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

45-45-90 Triangle Theorem: The length of the hypotenuse in a 45-45-90 triangle is times the length of a leg

30-60-90 Triangle Theorem: In a 30-60-90 triangle, the hypotenuse is two times the length of the shorter leg and the longer leg is times the length of the shorter leg.