31. Show that diagonals of a trapezium intersect proportionally.
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Answer:
trapezium ABCD in which AB∥DC and its diagonals AC and BD intersect at O.
To prove :
OC
AO
=
OD
BO
Construction :
Through O, draw EO∥AB, meeting AD at E.
Proof :
In △ADC,EO∥DC
Therefore,
ED
AE
=
OC
AO
.........(1)
In △DAB,EO∥AB
Therefore,
ED
AE
=
OD
BO
..........(2)
From 1 and 2, we get,
OC
AO
=
OD
BO
Hence, proved.
solution
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