In the given figure, ABCD is a trapezium. M and N are mid points of diagonals AC and BD respectively. Which of the following is true?
Construction: Join CN and produce it to meet AB at E.
In ΔCDN and ΔEBN, we have
DN = BN [since N is the midpoint of BD]
∠DCN=∠BEN [alternate interior angles]
and ∠CDN=∠EBN [alternate interior angles]
∴ ΔCDN≅ΔEBN [by AAS congruence rule]
∴ DC = EB and CN =NE [by CPCT rule]
Thus, in ΔCAE, the points M and N are the midpoints of AC and CE, respectively.
∴ MN || AE [by mid-point theroem]
⇒ MN || AB || CD