In the given figure, ABCD is a parallelogram. DC is produced to E so that DC = EC. If GF || DC, then FC is not always equal to

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C DC
Given that ABCD is a parallelogram.
∴ AB || DC and AB = DC
⇒ AB = EC (∵ DC = EC) …..(i)
Since AB || DC,
∠BAF = ∠CEF (Alternate interior angles) …..(ii)
In ΔBAF and ΔCEF,
∠BAF = ∠CEF [From (ii)]
∠BFA = ∠CFE (Vertically opposite angles)
AB = EC [From (i)]
∴ ΔBAF ≅ ΔCEF (AAS congruence rule)
⇒ BF = CF (CPCT) …..(iii)
Now, GF || DC and GD || FC
Thus, GDCF is a parallelogram.
∴ GD = CF …..(iv)
Also, AB || GF and AG || BF
Thus, AGFB is a parallelogram.
∴ AG = BF. …..(v)
From (iii), (iv) and (v), we get
FC = BF = GD = AG
Hence, the correct answer is option (c).

Suggest Corrections

Similar questions

Q. ABCD is a parallelogram, AD is produced to E so that DE = DC and EC produced meets AB produced in F. Prove that BF = BC

In the following figure, ABCD is a parallelogram and BC is produced to a point Q such that AD = CQ. If AQ intersect DC at P, then area of( $△$ BPC) equal to

In the following figure, ABCD is a parallelogram and BC is produced to a point Q such that AD = CQ. If AQ intersect DC at P, then:

Q. In the given figure ABCD is a parallelogram. Side DC is produced to E, and

∠

BCE

= 107^{o}

. Find

∠

∠

∠

∠

Q. ABCD is a parallelogram. AD is produced to E such that DE =DC. EC is produced to intersect AB produced in F.Prove that BF =BC.

Join BYJU'S Learning Program