Prove that any two perpendicular bisectors of two sides in a triangle must intersect.

Question

Prove that any two perpendicular bisectors of two sides in a triangle must intersect.

Please show picture and justify each step

Answer 1

I can't easily send you a picture, but I can tell you one process by which your proof can proceed.

Draw the perpendicular bisector of one side of the triangle.

Through the midpoint of another side, draw a line parallel to this perpendicular bisector.

This is the ONLY line parallel to the perpendicular and through the midpoint.

This line cannot be the perpendicular bisector of the 2nd side because it does not make a right angle with the 2nd side...it cannot do this because it is part of another right triangle.

Therefore, the 2 perpendicular bisectors are NOT parallel and must meet (intersect).