Question

PQRS is a parallelogram .B and D are midpoints of the sides QR and PS respectively.Show that ABCD is a parallelogram.
Figure

Answer 1

Let's draw diagonal PR.

Using midpoint theorem in triangle PSR,

DC | | PR & DC = PR/2 ... (1)

Similarly, in triangle PQR,

AB | | PR & AB = PR/2.... (2)

From (1) & (2),

AB | | PR & AB = CD.

So, □ ABCD is a parallelogram.