Question

In the picture below, two vertices of a parallelogram are joined to the

midpoint of two sides.​

Answer 1

Here AC and BD are diagonals and they bisect each other as we know.

Therefore we can say that AC is the median and passes through mid-poin of DB.

We know that

In any triangle, all the medians intersect at a single point and that point divides each median in the ratio 2:1 measured from vertex.

Therefore from triangle ABD,

We have

-------1

Similarly, from triangle BCD,

We have

;

----2

From 1 & 2

AG:GI:IC = AG:(GH + HI):IC

AG:GI:IC = 2:2:2 = 1:1:1

Hence the lines from vertices to mid-points of opposite side will divide the diagonal into three equal parts as shown above.

Hence proved.