Geometry 5-5, 5-6, 5-7 theorems

Converse of the Hinge Theorem

If two sides of one triangle are congruent to two side of another triangle and the 3rd sides are not congruent, then the larger included angle is across from the longer third side

phythagorean triple

A set of three nonzero numbers common Pythagorean triples a,b, and c such that a2+ b2= c2 ( three whole numbers) ex: 3, 4, 5

Angle side relationship in triangle: 5-5-2

If 2 angles of a triangle aren't congruent, then the longer side is opposite of the longer side

Angle-Side Relationships in Triangles: 5-5-1

If 2 sides of a triangle aren't congruent, then the larger angle is opposite the longer side

Hinge Theorem

If two sides of one triangle are congruent to two sides of another triangle and the included angles are not congruent, then the longer 3rd side is across from the larger incline angle

Pythagorean Inequalities Theorem

In triangle ABC, c is the length of the longest side

Converse of the Pythagorean Theorem

Is the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle

Triangle Inequality Theorem

The sum of any two side lengths of a triangle is greater than the side length