Construct a segment B'C of length BC and perpendicular to BC at C. Draw
B'B.
Find the midpoint M of BB'. Mark an arc of radius MB with center at B
to intersect the segment BC at pont N.
Now constuct a line parallel to AB through N. This line will intersect
AC at P and a parallel line to BC through P will intersect side AB Q. PQ
is the desired segment that divides the original triangle into equal areas.
Take any triangle ABC.
Construct a segment B'C of length BC and perpendicular to BC at C. Draw B'B.
Find the midpoint M of BB'. Mark an arc of radius MB with center at B to intersect the segment BC at pont N.
Now constuct a line parallel to AB through N. This line will intersect AC at P and a parallel line to BC through P will intersect side AB Q. PQ is the desired segment that divides the original triangle into equal areas.