Question

ABCD is a trapizium. M and N are the midpoints of AC and BD . Prove that MN parellel AB parallel DC and MN=1/2 (AB-DC).

Answer 1

Draw trapizium ABCD.given M&N are midpoints of AD&BC. join M&N, let the point of intersection of MN&DB be "0". Consider triangle ADB, OM IIAB as MN II AB &since "M" is midpoint of AD & half of it therefore OM =1/2AB , thus OM = 6 Now consider triangle BDC , N is mid-point of BCand is parallel to DC(since MN II DC). Now since MO=6 therefor ON=14-6 , =8. But since ON =1/2DC(mid point theorm therefore DC=2ON Therefore length of CD=16cm