Question

MP is the perpendicular bisector of the side AC of the triangle ABC, in which AB=AC. prove that about APB=2 Angle B

Answer 1

Since MP is perpendicular to AC, it follows:

angle AMP=angle CMP = 90°

let's call angle MPC=m

and also angle MCP = t

since AB=AC the triangle ABC is isosceles, thus

angle B = angle MCP = t

Finally, call APB= p

Since the angles forming a straight line must sum 180°, it follows that:

P + 90° - m + m = 180°

Simplifying:

P = 90°

Triangle ABP is right in P

This makes that m = 90 - m

and m=45°

Finally, since t = P - m

t = 45°

It follows that

angle APB = 2 ¨* angle B