Dan Finkel's diagram to demonstrate Maryam's Claim

The black triangle is divided by a line from a corner to the midpoint of the opposite side
Maryam said that whatever the shape of the trianlgle, this line will always split it in half.[br][br]Move the triangle around, buy moving the corners.[br][br]Do you agree with Maryam's claim?
– Simon Gregg1

Information: Dan Finkel's diagram to demonstrate Maryam's Claim