Theorem Theorem 6 11 Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side AB BC AC Proof Ex 47 p 342 AC BC AB A AB AC BC Ex 1 Tell whether a triangle can have sides with the given lengths Explain 3 5 7 Ex 2 Tell whether a triangle can have sides with the given lengths Explain 4 6 5 11 8 5 13 B Ex 3 The lengths of two sides of a triangle are 6 centimeters and 11 centimeters Find the range of possible lengths for the third side x 4 The lengths of two sides of a triangle are 22 inches and 17 inches Find the range of possible ngths for the third side