Mathematical proof that two triangles are congruent?

1, because AB=AC, BD=DC, and angle B= angle C.

So triangle ABD is equal to triangle ACD.

So angle BAD= angle CAD=45

Angle ABD= angle ADC=90,

The other angle C = 45

So the triangular ADC is an isosceles right triangle.

AD=DC

Because DE is perpendicular to DF

So angle AED+ angle ADF=90.

And because the angle ADF+ angle CDF=90.

So angle ADE= angle CDF

So ADE is equal to CDF

2. Because AED equals CFD.

So three AED = three CDF,

So s triangle bed +S triangle CDF=S triangle AED+S triangle bed =S triangle ABD.

Because AE=CF=6

So AB=AE+BE= 14.

AD=BD= 1/2*BC= seven twos.

So s triangle ABD=AD*DC/2=49.

And the s triangle AEF= 1/2*AE*AF=24.

S triangle ABC= 1/2*AB*AC=98.

So s triangle DEF=S triangle ABC-S three beds -S three CDF-S three AEF.

=98-49-24=25