Question

M is the midpoint of the side DC of a parallelogram ABCD. line BM intersects seg AC at point L line AD at point E. Prove that EL=2BL

Answer 1

GiVen ;-

∆ EDM and ∆ BCM are similar.

MD=CM => BC = DE,

as AD = BC,

AE = 2 BC

Similarily,,

ΔACL & ΔAEL are similar.

EL / BL = AE / BC = 2


So EL = 2 BL


thanks me Later ❤️

Answer 2

In ∆BMC and ∆EMD  

MC = MD ( As M is the midpoint of CD)

∠CMB = ∠ EMD ( Vertically opposite angles)

∠MBC = ∠ MED ( Alternate angles)

Thus, ∆BMC and ∆EMD  are similar

As, AD = BC and BC = DE

AD + DE = BC + BC

AE = 2BC

Similarly ΔCBL & ΔAEL will be similar.

EL / BL = AE / BC = 2

EL / BL = 2BC / BC

EL / BL = 2

Hence, EL = 2 BL