Half The Area of a Triangle:
Cut by a Line Through an Arbitrary Point on One Side

Problem 1.

Let D be any point on a side of triangle ABC. Construct a line through D that divides the triangle into two equal areas. When D corresponds to a vertex or to a midpoint, then a line along the median will suffice. Assume D does not necessarily correspond to a vertex or a midpoint.



Problem 2.

Construct the triangle with its extended sides and let the constucted line through D cut off, with lines AB and BC, a triangle half the area of the original regardless of whether D is between B and C.

A GSP Sketch

Trace the midpoint of the segment cut off by the two sides (perhaps extended) of the triangle.

A GSP Sketch

Or, trace an envelope of the lines through D as D is animated along BC.

A GSP Sketch

Return to the EMAT 4600/6600 Page