Question

X and Y are points on the side LN of the triangle LMN such that LX = XY = YN. Through X, a line is drawn parallel to LM to meet MN at Z (See figure). Prove that ar (LZY) = ar (MZYX)

Answer 1

Given: X and Y are points on the side LN such that LX = XY = YN and XZ || LM

To prove: ar (ΔLZY) = ar (MZYX)

Proof: Since, ΔXMZ and ΔXLZ are on the same base XZ and between the same parallel lines LM and XZ.

Then, ar (ΔXMZ) = ar (ΔXLZ)  ...(i)

On adding ar (ΔXYZ) both sides of equation (i), we get

ar (ΔXMZ) + ar (ΔXXZ) = ar (ΔXLZ) + ar (ΔXYZ)

⇒ ar (MZYX) = ar (ΔLZY)

Hence proved.