Through the mid-point M of the side CD of a parallelogram ABCD, the line BM is drawn intersecting AC in L and AD…

CBSE Class 10 Maths PYQ · Triangles · Similarity with Quadrilaterals · 5 Marks · March 2024 · Standard

Solve it yourself first — then press ↓ or tap Show Solution. Use ← → for previous / next question.

1415 Marks · March 2024 · Standard

Through the mid-point M of the side CD of a parallelogram ABCD, the line BM is drawn intersecting AC in L and AD produced in E. Prove that EL = 2BL.

Show SolutionHide Solution↓

Correct fig.
In $\triangle BLC$ and $\triangle ELA$
$\frac{BL}{EL} = \frac{BC}{EA} \dots(i)$
DM $||$ AB
$\therefore$ AD = DE
$\Rightarrow AE = 2AD$
$\Rightarrow AE = 2BC \dots(ii)$
From (i) and (ii)
$EL=2BL$