Question

Parallelogram ABCD is given. Draw line EF so that it goes through the vertex A. Point E lies on the side BC and point F lies on the extension of DC . Prove that △ABE∼△FCE.

Answer 1

Answer:

Given: ABCD is a parallelogram,

In which E ∈ BC and F lies on the extension of DC,

Such that line segment EF goes through the vertex A.

To prove: $\triangle ABE\sim \triangle FCE$

Proof:

Since, By the definition of parallelogram,

$DC\parallel AB \implies DF\parallel AB$

By the Alternative interior angle theorem,

$\angle CFE\cong \angle EAB$

Also, $\angle CEF\cong \angle BEA$ ( vertically opposite angles )

Thus, By AA similarity postulate,

$\triangle ABE\sim \triangle FCE$

Hence proved.