Question

JKLM is a trapezium where JK || ML. If the diagonals MK and JL intersect each other at N, then the value of MK $\times$ NL is always equal to

• A. ML $\times$ JK
• B. MJ $\times$ KL
• C. MN $\times$ JL
• D. KM $\times$ JL

Answer 1

The correct option is C MN $\times$ JL

Since the diagonals of trapezium divide each other proportionally.

$\therefore \frac{NK}{MN}=\frac{JN}{NL}$
Adding 1 on both the sides
$\Rightarrow \frac{NK}{MN}+1=\frac{JN}{NL}+1$
$\Rightarrow \frac{NK+MN}{MN}=\frac{JN+NL}{NL}$
$\Rightarrow \frac{MK}{MN}=\frac{JL}{NL}$
$\Rightarrow MK\times NL=MN\times JL$
Hence, the correct answer is option (3).