ABCD is a trapezium with AB || DC.A parallel to AC cuts the line AB at X and BC at Y. Prove that ar (ADX) = ar (ACY)

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

ABCD is a trapezium with A B" "||" "D C . A line parallel to AC intersects AB at X and BC at Y. Prove that a r" "(A D X)" "=" "a r" "(A C Y) .

ABCD is a trapezium with AB //DC. A line parallel to AC intersects AB at point M and BC at point N. Prove that: area of triangleADM=area of triangleACN.

In the given figure ABCD is a trapezium with AB || DC. E and F are respectively midpoint of AD and BC. Prove that, EF=1/(2)(AB+CD)

In Figure,BC|XY,BX|CA and AB||YC Prove that: ar(ABX)=ar(ACY)

Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O. Prove that ar( Delta AOD) = ar( Delta BOC).

ABCD is a trapezium in which AB I I DC. DC is produced to E such tha t CE= AB, prove that ar( Delta ABD) = ar( Delta BCE).

ABCD is a parallelogram whose diagonals AC and BD intersect at O. A line through O intersects AB at P and DC at Q. Prove that ar (Delta POA) =" ar "(Delta QOC) .

In Fig.4.123, ABCD is a trapezium with AB||DC. If Delta AED is similar to Delta BEC, prove that AD=BC .

Diagonals AC and BD of a trapezium ABCD with AB| DC intersect each other at O . Prove that ar(AOD)=ar(BOC)