How do i write a mathmatical proof?

I can give you an example of how to write a formal geometrical proof, but I don’t understand the precise nature of your particular question. Two right-angled triangles within one, creating a square in the middle?

A formal proof should include:

(a) an appropriately lettered diagram showing what is given and any constructions performed;

(b) a statement of what is given in relation to the particular diagram you have drawn;

(c) a statement of what is to be proved in relation to the diagram;

(d) a description of any construction performed;

(e) the argument used to prove the theorem;

(f) a statement of the conclusion.

Diagram:

(cannot draw that here).

Given:

A triangle ABC with angle ACB = angle ABC.

Prove:

AC = AB.

Construction:

Draw a line AD bisecting angle BAC, and let this meet CB at D.

Proof:

In the triangles ACD, ABD:

Angle ACD = Angle ABD (given)

Angle CAD = Angle BAD (construction)

AD = AD (common)

Therefore triangle ACD is congruent (AAS) to triangle ABD, and in particular, AC = AB.

I agree with rackbrain

The measures of the corresponding angles and sides must be equal in order for the triangles to be congruent by definition..