Question

In the given figure, O is the middle point of both AB and CD. Prove that AC = BD and AC || BD.

Answer 1

In Δ’s AOC and BOD

OA = OB

OC = OD

∠AOC = ∠BOD (vertically opposite angles)

ΔAOC = ΔBOD (by SAS congruence property)

Hence AC = BD (by c.p.c.t)

Also ∠OAC = ∠OBD (alt. angle)

AC || BD

Hence proved.