Question

How do you prove this?

Answer 1

Answer:

Show ΔBCD ≅ ΔGFE, so ∠C ≅ ∠F. Base angle of an isosceles triangle are congruent, so ΔACF is isosceles.

Step-by-step explanation:

Informally, subtract DE from CE and DF. This will show CD ≅ EF.

Then ΔBCD ≅ ΔGFE by the HL theorem for right triangles.

Corresponding parts of congruent triangles are congruent, namely the angles C and F.

Since base angles of ΔACF are congruent, it is isosceles.