Question

Given: ABCD is a ∥-gram, BF ⊥ CD , BE ⊥ AD, Prove: △ABE∼△CBF

Answer 1

Answer:

Hence proved △ABE∼△CBF.

Step-by-step explanation:

Given,

ABCD is a parallelogram.

BF ⊥ CD    and

BE ⊥ AD

To Prove : △ABE∼△CBF

We have drawn the diagram for your reference.

Proof:

Since ABCD is a parallelogram,

So according to the property of parallelogram opposite angles are equal in measure.

$\therefore m\angle A = m\angle B$ ⇒1

And given that BF ⊥ CD and BE ⊥ AD.

So we can say that;

$m\angle F=m\angle E=90\°$ ⇒2

Now In △ABE and △CBF

∠A = ∠C   (from 1)

∠E = ∠F    (from 2)

So by A.A. similarity postulate;

△ABE∼△CBF