Converse of Triangle Inequality Theorem Use the Two Circle Theorem (Problem 21) to prove i...

Converse of Triangle Inequality Theorem Use the Two Circle Theorem (Problem 21) to prove in absolute geometry that if three numbers a, b, and c satisfy the (strict) Triangle Inequality (that is, a + b > c, a + c > b, and b + c > a), then there exists a triangle ∆ABC having a, b, and c as the lengths of its sides. Thus,

COROLLARY: Given a segment , there exists an equilateral triangle ∆ABC having  as base.