Bisecting a Triangle

By: Tim Lehman

**Exploration 1: Dividing a triangle into
two triangles of equal area**

**Method I**: The
most obvious way to divide a triangle into two equal halves is
to construct the median from one of the vertices of the triangle
to the midpoint of the opposite side, as below. Each of the medians
would split the triangle into two equal halves.

**Click here**** **if you are wondering why
the medians bisect the triangle.

**Method II:** Other
segments exist that divide the triangle into two equal parts.
In this section, we will find a segment with not only this charactistic
but is also parallel to a side of the triangle.

The segment is DE in the above diagram. Need
**a hint** in finding segment DE? For
an explanation on how to find DE, **click
here**.

**Method III:** In
this section, we will divide the triangle into pieces are half
the triangle when added together. In the drawing below, the triangle
has been bisected into the blue quadrilateral and the two green
triangles.

There are several variations of the above diagram. The triangle could be divided in half by selecting two of the four triangles (see diagram below) created by connecting the midpoints of the sides.

Unsure why this works? **Click
here**.