A farmer had a plot in the shape of a parallelogram. He divided into three equal parts, each of which was a separate parallelogram. He then gave his son one-third of the land. The son, who realized that the district in which he lived had no school, decided to set one school up in his plot, given to him by his father.

(i) Show how the proposal of the farmer can be implemented, with the help of a diagram. How much part of the land does the son get? Justify the proposal.

To implement the proposal of the farmer, we need to divide the original parallelogram into three equal parts, and then give one-third of the land to the son.

First, let's draw a diagram to visualize the situation. Draw a parallelogram representing the original plot of land. Label it as ABCD, where AB is parallel to CD and AD is parallel to BC.

Next, divide the parallelogram ABCD into three equal parts. To do this, draw two lines parallel to AB and CD, dividing the parallelogram into three smaller parallelograms with equal areas. Label these smaller parallelograms as PQR, RST, and TUW.

Now that the land has been divided into three equal parts, we need to give the son one-third of the land. In this case, the son will receive the parallelogram RST.

To justify the proposal, we consider that the original land was divided into three equal parts. Each of these parts, represented by PQR, RST, and TUW, has the same area.

Since the son receives one of these three equal parts, which is the parallelogram RST, it means he receives one-third of the total land area. Therefore, the son gets one-third of the land.

By giving his son one-third of the land, the farmer is ensuring an equal distribution of the property among his children.

Note: The diagram and justification provided are based on the assumption that the original land is a parallelogram and is divided into three equal parts, as stated in the question.