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CBSE Class 9 Answered

mathematics doubt
Asked by | 08 Mar, 2012, 06:33: AM
answered-by-expert Expert Answer
Let there be a trapezium ABCD , AB||CD
Draw a line BE parallel to AD meeting DC at E
I cn be seen that ABED is a parallelogram as both pairs of opposite sides are parallel ,
Hence angleA = angleE 
Also Since ABCD is cyclic so angleA + angleDCB = 180
Hence we get angleE = 180 - angleDCB = angle ECB
Thus BE = BC = AD
This proves that the trapezium is iscoceles.
Also it can be proved that triangles ABD and ABC are congruent by SAS
Thus diagonals AC = BD by C.P.C.T. 
Answered by | 08 Mar, 2012, 07:14: AM

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