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

ABCD is a square. E and F are respectively the mid-points of BC and CD. If R is the mid-point of EF (Fig. 9.15), prove that ar (AER) = ar (AFR)

In Fig. 9.23, BD || CA, E is mid-point of CA and BD = 1/2 CA. Prove that ar (ABC) = 2ar (DBC)

In Fig. 9.24, CD || AE and CY || BA. Prove that ar (CBX) = ar (AXY)