ABCD is a quadrilateral and M,N,O,P …

Given: ABCD is a quadrilateral and M,N,O and P are mid points of AB,BC,CD and AD respectively . To Prove: MNOP os a llgm. Construction: Draw AC and BD. Proof: In triangle ABC, M is the mid-point of AB and N is the mid point of BC. Therefore, MN II AC and MN=1/2 of AC (MPT)...(1) Similarly, In triangle ACD, PO II AC and PO=1/2 of AC (MPT)...(2) Similarly, In triangle ADB, PM II BD and PM=1/2 of BD (MPT)...(3) Similarly, In triangle BCD, ON II BD and ON=1/2 of BD (MPT)...(4) From 1,2,3 and 4 MN II PO and NO II PM Therefore, MNOP is a llgm ( If in a quadrilateral 2 pair of opposite sides are parallel then it is a llgm) H.P.