If X is the midpoint of the side BC of a parallelogram ABCD ,DX meets AC in Y Prove that - Maths - Areas of Parallelograms and Triangles

Question

If X is the midpoint of the side BC of a parallelogram ABCD ,DX
meets AC in Y Prove that ar(triangle ADY) = AR(triangle DYC)

Tushar Kohli · Accepted Answer

The triangles AYD and XYC can easily be proved to be similar (by
AAA)
Also, AD = 2XC as X is the midpoint of BC
Hence, AY: YC = 2: 1 as well (as ratio is same for similar
triangles)
Hence, area (ADY): area (DYC) = 2: 1 (triangles on the same base
and the same height have area in the ratio of the bases)
So what the question has asked to prove is wrong Please check the
question again and the solution given

If X is the midpoint of the side BC of a parallelogram ABCD ,DX meets AC in Y.Prove that ar(triangle ADY) = AR(triangle DYC)