Q. 11

# ABCD is a parallelogram and E is a point on BC. If the diagonal BD intersects AE at F, prove that AF × FB = EF × FD.

Answer :

Given that, AB ∥ DC & AD ∥ BC

To Prove: AF × FB = EF × FD

Proof: In ∆DAF & ∆BEF

∠DAF = ∠BEF [∵ they are alternate angles]

∠AFD = ∠EFB [∵ they are vertically opposite angles]

This implies that ∆DAF ∼ ∆BEF by AA-similarity criteria.

⇒

Now cross-multiply them,

AF × FB = FD × EF

Hence, proved.

Rate this question :

How useful is this solution?

We strive to provide quality solutions. Please rate us to serve you better.

Related Videos

Basic Proportionality Theorem42 mins

A Peep into Pythagoras Theorem43 mins

R.D Sharma | Solve Exercise -4.2 and 4.3FREE Class

NCERT | Strong Your Basics of Triangles39 mins

RD Sharma | Imp. Qs From Triangles41 mins

Quiz | Criterion of Similarity of Triangle45 mins

How to Ace Maths in NTSE 2020?36 mins

Know About Important Proofs in Triangles33 mins

Master BPT or Thales Theorem39 mins

Champ Quiz | Thales Theorem49 mins

Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Expertsview all courses

Dedicated counsellor for each student

24X7 Doubt Resolution

Daily Report Card

Detailed Performance Evaluation