CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
Question

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

[Hint : Join CX.]


Open in App
Solution

proving that ar(ADX)=ar(ACY):
Given:

ABCD is a trapezium with,ABDC,XYAC

Construction:

Join CX

Proof:

ar(ΔADX)=ar(ΔAXC)————(1) (They are on the same baseAX and in-between the same parallels AB and CD)

ar(ΔAXC)=ar(ΔACY)_______________(2) (They are on the same base AC and in-between the same parallels XY and AC)

From equations (1) and (2),

ar(ΔADX)=ar(ΔACY)

Hence we prove that ar(ΔADX)=ar(ΔACY)


flag
Suggest Corrections
thumbs-up
1
BNAT
mid-banner-image