In Fig
, `AP II BQ II CR`. Prove that ar (AQC) = ar (PBR).

AP||BQ||CR. Prove that ar(AQC) = ar(PBR)

In Fig. 9.13, ABCD is a parallelogram and EFCD is a rectangle. Also, AL bot DC . Prove that (i) ar (ABCD) = ar (EFCD) (ii) ar (ABCD) = DC × AL

ABCD is a trapezium with AB || DC. A line parallel to AC intersects AB at X and BC at Y. Prove that ar (ADX) = ar (ACY). [Hint : Join CX.]

ABCD is a squre. E and F are respectivley the mid-points of BC and CD. If R is the mid-points of EF. Prove that ar (AER) = ar(AFR).

In the figure CD||AE and CYA||BA. Prove that : ar(CBX) = ar(AXY)

In the figure ABCDE is any pentagon. BP drawn parallel to AC meets DC produced at P and EQ drawn parallel to AD meets CD produced at Q. Prove that : ar(ABCDE) = ar(APQ)

In trapezium ABCD, AB ||DC and L is the mid-point of BC. Through AL, a line PQ||AD has been drawn which meets AB at P and DC produced to Q. Prove that : ar(ABCD) = ar(APQD)

In Fig. 9.24, ABC and ABD are two triangles on the same base AB. If line- segment CD is bisected by AB at O, show that ar(ABC) = ar (ABD).

ABCD is a trapezium in which AB||DC, DC = 30 cm and AB = 50 cm. If X and Y are, respectivley that mid-points of AD and BC, prove that ar(DCYX) = 7/9 ar(XYBA)

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