P is a point on side BC of a parallelogram ABCD. If DP produced meet AB produced at point L, then
$D P : P L = D C : B L$

True

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

False

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

Open in App

Solution

The correct option is A True
Given: $A B C D$ is a parallelogram
In $△ L A D$ ,
$B P | | A D$ (Given $A B C D$ is a parallelogram and $P$ lies on $B C$ )
$∴$ , $\frac{L B}{B A} = \frac{L P}{P D}$ (Basic proportionality theorem)
or $\frac{A B}{B L} = \frac{D P}{P L}$ (Taking reciprocals)
or $\frac{D C}{B L} = \frac{D P}{P L}$ (Since, $A B = D C$ (opposite sides of parallelogram)

Suggest Corrections

Similar questions

P is a point on side BC of a parallelogram ABCD. If DP produced meets AB produced at point L, prove that:

I)DP:PL=DC:BL

ii)DL:DP =AL:DC

D L : D P = A L : D C

\frac{D P}{P L} = \frac{D C}{B L}

\frac{D L}{D P} = \frac{A L}{D C}

In the adjoining figure ABCD is a parallelogram. ‘P’ is a point on BC, DP and AB are produced meet at L. Prove that DP : PL = DC : BL.

Join BYJU'S Learning Program