Q.1 ABCD is a parallelogram. AB is produced tobisects BC.

1.	Q.1 ABCD is a parallelogram. AB is produced tobisects BC.
Answer» Given, ABCD is a parallelogram. BE = AB To show, ED bisects BC Proof: AB = BE (Given) AB = CD (Opposite sides of \|\|gm) ∴ BE = CD Let DE intersect BC at F. Now, In ΔCDO and ΔBEO, ∠DCO = ∠EBO (AE \|\| CD) ∠DOC = ∠EOB (Vertically opposite angles) BE = CD (Proved) ΔCDO ≅ ΔBEO by AAS congruence condition. Thus, BF = FC (by CPCT) Therefore, ED bisects BC. Proved

Answer»

Given,

ABCD is a parallelogram.

BE = AB

To show,

ED bisects BC

Proof:

AB = BE (Given)

AB = CD (Opposite sides of ||gm)

∴ BE = CD

Let DE intersect BC at F.

Now,

In ΔCDO and ΔBEO,

∠DCO = ∠EBO (AE || CD)

∠DOC = ∠EOB (Vertically opposite angles)

BE = CD (Proved)

ΔCDO ≅ ΔBEO by AAS congruence condition.

Thus, BF = FC (by CPCT)

Therefore, ED bisects BC. Proved

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