2. Application of median of a triangle

In  your home, your mom cooked Mexican hexagon pizza (as in the picture given below).

 

 

While your mom offers a pizza slice to you, your friend joins you at your home.

 

You then choose to share your pizza slice with your friend.

 

How will you divide the pizza slice so that each of you get an equal amount to eat?

 

To solve this issue, we use a remarkable idea called MEDIAN.

 

Let the corners of the pizza piece be \(A\), \(B\), and \(C\).

 

 

From any interior angle (say \(\angle A\)) of the \(\triangle ABC\), cut till the midpoint of the opposite side (say \(D\)) so that you will have an equal amount of pizza (\(ADB\) and \(ADC\)) for you and your friend.

 

Imagine two more friends entering the scene.

 

You should again use the concept of MEDIAN. Cut the pizza slice along a different median. That is, from any interior angle to the midpoint of the opposite side. For example, cut from \(D\) to the midpoint \(E\) of \(AC\), and cut again from \(D\) to the midpoint \(F\) of \(AB\).

 

 

Thus, you have successfully cut the pizza slice into four equal parts.

 

You can now happily enjoy your pizza-time with your friends.