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in ∆ABC,DAE is a straight line parallel to BC such thay DA=AE.if CD meets AB at X and BE meets AC at Y prove that XY is parallel to BC.

in ∆ABC,DAE is a straight line parallel to BC such thay DA=AE.if CD meets AB at X and BE meets AC at Y prove that XY is parallel to BC.

Grade:12th pass

1 Answers

Amit jha
38 Points
4 years ago
Since, triangle DAC and EAC are in the same base (since , DA = EA ) and b/w same parallels DE and BC => ar( DAC )= ar ( DAC ) =>ar(DAC - AXY ) = ar ( EAC - AXY ) =>ar(XBY) = ar(YCX ) Since, triangles XBY and YCX are on the same base and having same area => XY is parallel to BC ( converse of mid point theorem)

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