Diagonals of parallelogram ABCD intersect at O as shown in Fig. 17.30. XY contains O, and x,Y are points on opposite sides of the parallelogram. Give reasons for each of the following:

Question

Diagonals of parallelogram ABCD intersect at O as shown in Fig. 17.30. XY contains O , and x,Y are points on opposite sides of the parallelogram. Give reasons for each of the following:

Philoid · Accepted Answer

(i) OB = OD

OB = OD [In a parallelogram diagonals bisect each other]

(ii) ∠OBY =∠ODX [Alternate interior angles are equal]

(iii) ∠BOY= ∠DOX [Vertically opposite angles are equal]

(iv) ΔBOY ≅ ΔDOX

In ΔBOY and ΔDOX

OB = OD [In a parallelogram diagonals bisect each other]

∠OBY =∠ODX [Alternate interior angles are equal]

∠BOY= ∠DOX [Vertically opposite angles are equal]

ΔBOY ≅ΔDOX [ASA rule]

Now, state if XY is bisected at O.

Hence OX = OY [Corresponding parts of congruent triangles]