Question

Given: ABCD is a ∥-gram; DE ∩ AB =F
Prove: △ADF∼△CDE

Answer 1

By AA similarity

Explanation:

We have been given that ABCD is a parallelogram

So, by the property of parallelogram AB ||CD and FD is cutting the line BC

Hence, FD is transverse line. In transverse line alternate angles are equal.

Therefore, ∠AFD=∠EDC (alternate interior angles)

And ∠FAD=∠ECD (opposite angles in parallelogram)

Therefore, by AA similarity △ADF∼△CDE