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

Asked by Sthitaprajna Mishra | 4th Feb, 2014, 07:47: PM

Expert Answer:

We know that two triangles on the same base and between the same parallels are equal in area.
 
Consider the following figure.
 
In the above figure, triangle ADX and ACX are on the same base AX and between the parallels AB and DC.
 
Therefore, ara r left parenthesis triangle A D X right parenthesis equals a r left parenthesis triangle A C X right parenthesis .,..(1)
Similarly, triangle ACX and ACY are on the same base AC and between the parallels XY and AC.
 
Therefore, a r left parenthesis triangle A C X right parenthesis equals a r left parenthesis triangle A C Y right parenthesis ....(2)
From equations (1) and (2), we have
 
a r left parenthesis triangle A D X right parenthesis equals a r left parenthesis triangle A C Y right parenthesis

Answered by  | 5th Feb, 2014, 11:04: AM

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