Question

In Figure, ABCD is a parallelogram in which P is the mid-point of DC and Q is a point on AC such
that CQ = (1/2) AC. If PQ produced meets BC at R, prove that R is a mid-point of BC.

Answer 1

Answer:

Step-by-step explanation:

Construction: Join BD to intersect AC at O

Proof: ∵ AO = OC = 1/2 AC

Now, CQ = 1/4 AC

               = 1/4(2*OC)

               = OC/2

• Q is the midpoint of CO

In ∆CDO,

∵ P is the midpoint of DC and Q is the midpoint of CO

∴ PR parallel DB and QR parallel OB

Now, in ∆COB,

∵ Q is the midpoint of CO and QR parallel OB

∴ R is the midpoint of BC

*By converse of Midpoint theorem