Abcd is a trapezium with ab parallel to dc

Asked by admin @ 10/08/2021 in Math viewed by 297 People

"Question 13 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.]

Class 9 - Math - Areas of Parallelograms and Triangles Page 164"

Answered by admin @ 10/08/2021

Two Triangles on the same base and between
the same parallels are equal in area.

==========================================================

Given,

ABCD is a
trapezium with AB || DC & XY || AC

Construction,

Join CX .

To Prove,

ar(ADX) =
ar(ACY)

Proof:

ar(△ADX) =
ar(△AXC) —
(i)

(On the
same base AX and between the same parallels AB and CD)

also,

ar(△ AXC)=ar(△ ACY) — (ii)

(On the same base AC and between the same
parallels XY and AC.)

From (i) and (ii),

ar(△ADX)=ar(△ACY)

=========================================================

Hope
this will help you...

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