Question

13. ABCD is a trapezium with AB || DC. A line parallel to AC intersects AB am
at Y. Prove that ar (ADX)= ar (ACY).
A А
P
[Hint: Join CX.]​

Answer 1

Answer:

Step by Step Explanation::-

• GIVEN---:

A TRAPEZIUM ABCD WHERE ABIICD & ACIIXY

• TO PROVE---:

AR(ADX)=AR(ACY)

• CONSTRUCTION---:

JOIN XC

• PROOF---:

FOR ∆ACX & ∆ACY LIE ON THE SAME BASE AC & ARE BETWEEN PARALLEL LINES AC & XY.

SO,AR(ACX)=AR(ACY) .....1

ALSO, ∆ACX AND ∆ADX LIE ON THE SAME BASE AX AND ARE BETWEEN PARALLEL LINES AX & DC.

SO,AR(ACX)=AR(ADX) ......2

FROM EQUATION 1 & 2,

AR(ACY)=AR(ADX)

HENCE PROVED