Q. 18

ABCD is a paralle A. 45°

B. 60°

C. 90°

D. 75°

Answer :

ABCD is a parallelogram. BD is the diagonal and M is the mid-point of BD.

BD is a bisector of B


We know that,


Diagonals of the parallelogram bisect each other


Therefore,


M is the mid-point of AC


AB || CD and BD is the transversal,


Therefore,


ABD = BDC (i) (Alternate interior angle)


ABD = DBC (ii) (Given)


From (i) and (ii), we get


BDC = DBC


In Δ BCD,


BDC = DBC


BC = CD (iii) (In a triangle, equal angles have equal sides opposite to them)


AB = CD and BC = AD (iv) (Opposite sides of the parallelogram are equal)


From (iii) and (iv), we get


AB = BC = CD = DA


Therefore,


ABCD is a rhombus


AMB = 90° (Diagonals of rhombus are perpendicular to each other)

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