The Median Of Triangle Divides It Into Two

The Median Of Triangle Divides It Into Two. Hence the name and hence a triangular object of uniform density would balance on any median. In ΔABC AD is the median.

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In the figure AD is the median that divides BC into two equal halves that is DB DC. The median of a triangle divides it into triangle of equal area. Show that a median of a triangle divides it into two triangles of equal areas.

Each median divides the area of the triangle in half.

To show that this is always true we can write a short proof. In fact the 3 medians divide the triangle into 6 smaller triangles of equal area. A median is the line from a midpoint of a side to the opposite vertex. Hence the name and hence a triangular object of uniform density would balance on any median.