THEOREMS OF TRIANGLE INEQUALITY

A

2

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

Triangle Inequality Theorem 3 (S1 +S2 >S3)

2

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

Exterior Angle Inequality Theorem

2

If two sides of one triangle are congruent to two sides of another triangle, but the included angle of the first is larger than the included angle of the second triangle then the third side of the first triangle is longer than the third side of the second triangle. What theorem is this?

Hinge Theorem

B

2

What is the formula in finding the range of the third side? 

DIFFERENCE < X < SUM 

2

If one side of a triangle is longer than a second side, then the angle opposite the longer side is larger than the angle opposite the shorter side. What theorem is this?

Triangle Inequality Theorem 3 (Ss→Aa) or Side -Angle Relationship Theorem 

2

If two sides of one triangle are congruent to two sides of another triangle, but the third side of the first triangle is greater than the third side of the second triangle, then the included angle of the first triangle is larger than the included angle of the second triangle.

Converse of the Hinge Theorem.

C

2

What theorem is this?
If one angle of a triangle is larger than a second angle, then the side opposite the larger angle is longer than the side opposite the smaller angle. 

Triangle Inequality Theorem 2 (Aa→Ss) or Angle Side Relationship Theorem

2

The total sum of the interior angle?

180⁰

2

What is the sum of two linear pairs?

180⁰