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 Fig.). Prove that ar (LZY) = ar (MZYX)

Answer 1

According to the question,

LX = XY = YN

XZ II LM

We have,

ar(LZX) + (XZY) = ar(LZY)               — (1)

ar(MXZ) + ar(XZY) = ar(MZYX)        — (2)

Both triangles LZX and MXZ are on the same base XZ and between same parallels LM and XZ

ar(LZX) = ar(MXZ)

Adding equation (1) and (2),

We get,

ar(LZY) = ar(MZYX)

Hence proved