Mark P inside square ABCD, so that triangle ABP is equilateral. Let Q be the intersection of BP with diagonal AC. Triangle CPQ looks isosceles. Is this actually true?

If AB = BC, must point B be the midpoint of AC? Explain.

Classify the triangle with vertices A(2,1), B(4,5) and C(6,1) as isosceles or equilateral. Use distance formula to justify your answer. Round answers to tenths if needed. Side AB has length , side BC has length , side AC has length These side lengths support the fact that triangle ABC is