Question

ABCD is a parallelogram,P is a point on sides BC DP when produced meets AB produced to L,prove that

i]DP/PL = DC/BL ii] DL/DP=AL/DC

Answer 1

using some theorems these question can be solved easily

Answer 2

$\bold{\frac{D P}{P L}=\frac{D C}{B L}}$ and $\bold{\frac{D L}{D P}=\frac{A L}{D C}}$  are proven in parallelogram of ABCD.

Solution:                                                  

Let ABCD be a parallelogram and L extended to prove that $\frac{D P}{P L}=\frac{D C}{B L}$

Let us first show that in triangle PCD and BPL, the angle of DPC and BPL are same as they are vertically opposite to each other.

The angle C = B, as they are alternate angle, therefore it shows that triangle PCD and BPL are similar in nature, therefore sides DP = PL and DC = BL.

$\bold{\frac{D P}{P L}=\frac{D C}{B L}}$Hence Proved

Now it can be said that as AB = DC, due to parallel sides of a parallelogram, it is known that  

$\frac{D P+P L}{D P}=\frac{A B+B L}{D C}$

Hence, $\bold{\frac{D L}{D P}=\frac{A L}{D C}}$ Proved