Question

prove that the diagonals of a parallelogram bisect each otherm​

Answer 1

ABCD is a parallelogram, diagonals AC and BD intersect at O.

In triangles AOD and COB,

DAO = BCO (alternate interior angles)

AD = CB.

ADO = CBO (alternate interior angles)

AOD COB (ASA)

Hence, AO = CO and OD = OB (c.p.c.t)

Thus, the diagonals of a parallelogram bisect each other

Answer 2

Answer:

ABCD is a parallelogram, diagonals AC and BD intersect at O

In triangles AOD and COB,

DAO = BCO                               (alternate interior angles)

AD = CB

ADO = CBO                               (alternate interior angles)

AOD COB                           (ASA)

Hence, AO = CO and OD = OB          (c.p.c.t)

Thus, the diagonals of a parallelogram bisect each other.

Step-by-step explanation: