Question

ABCD is a parallelogram. take point E on the side AB, such that BE=AB then prove that BC bisects DE.​

Answer 1

ABCD is a parallelogram.

⇒ AB || CD

⇒ AE || CD,

CB is the transversal

⇒ ∠3 = ∠4 (alt. ∠s are equal)

Now in Δs OCD and OBE,

CD = AB = BE

∠2 = ∠1 (Vertically opposite ∠s)

∠3 = ∠4 (Proved above)

∴ ΔOCD ≅ ΔOBE (AAS)

⇒ BO = OC ⇒ O is the mid-point of BC

⇒ ED bisects BC.

Proved