In the given figure, ABCD is a parallelogram, E is a point on BC and the diagonal BD intersects AE at F. Prove that : DF X FE=FB x FA. please don't spam or else you shall be reported.

In the given figure, ABCD is a parallelogram, E is a point on BC and t

1.	In the given figure, ABCD is a parallelogram, E is a point on BC and the diagonal BD intersects AE at F. Prove that : DF X FE=FB x FA. please don't spam or else you shall be reported.
Answer» <html><body><p>hat, the diagonal BO of parallelogram ABCD intersects the segment AE at F, where <a href="https://interviewquestions.tuteehub.com/tag/e-444102" style="font-weight:bold;" target="_blank" title="Click to know more about E">E</a> is any <a href="https://interviewquestions.tuteehub.com/tag/point-1157106" style="font-weight:bold;" target="_blank" title="Click to know more about POINT">POINT</a> on BC.To prove: DF×EF=FB×FABased on the given information, we can draw the figure shown above.Now, in △AFD and △BFE,⇒ ∠FAD=∠FEB [ <a href="https://interviewquestions.tuteehub.com/tag/alternate-373425" style="font-weight:bold;" target="_blank" title="Click to know more about ALTERNATE">ALTERNATE</a> angles ]⇒ ∠AFD=∠BFE [ <a href="https://interviewquestions.tuteehub.com/tag/vertically-3260386" style="font-weight:bold;" target="_blank" title="Click to know more about VERTICALLY">VERTICALLY</a> opposite angles ]∴ △ADF∼△BFE [ By AA similarity ]∴ FADF= EFFB∴ DF×EF=FB×FA[Hence <a href="https://interviewquestions.tuteehub.com/tag/proved-7287273" style="font-weight:bold;" target="_blank" title="Click to know more about PROVED">PROVED</a>]</p></body></html>