Question

Explain, why

ΔABC ≅ ΔFED

Answer 1

Given that, ∠ABC = ∠FED (1)

∠BAC = ∠EFD (2)

The two angles of ΔABC are equal to the two respective angles of ΔFED. Also, the sum of all interior angles of a triangle is 180º. Therefore, third angle of both triangles will also be equal in measure.

∠BCA = ∠EDF (3)

Also, given that, BC = ED (4)

By using equation (1), (3), and (4), we obtain

ΔABC ≅ ΔFED (ASA criterion)