How do i prove this

[Loki123]

I remember proving this but I can't remember how.
This triangle has two same sides and one 90 degree angle. From the point B there is a bisector of the angle that creates point M on the line AC that is the opposite to point B. Two squares are constructed on top of AC, each using AM and MC as the base. Prove the the surface area is two times bigger in one than the other (that's P in my written work)

 

[Dr.Peterson]

I remember proving this but I can't remember how.
This triangle has two same sides and one 90 degree angle. From the point B there is a bisector of the angle that creates point M on the line AC that is the opposite to point B. Two squares are constructed on top of AC, each using AM and MC as the base. Prove the the surface area is two times bigger in one than the other (that's P in my written work) View attachment 30578

This is very easy to prove using the theorem stated and proved here:

Angle Bisector Theorem - MathBitsNotebook(Geo)

mathbitsnotebook.com

Otherwise, I would probably think about half-angle formulas.

 

[lev888]

Construct a height in the triangle AMB from point M.