swastik pramanik
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sir i am not able to prove that O1O2 || BC. please give some hint.
sir i think angles can be anything in equilateral polygon.
NOTE: In the question angle CXY should be angle CYX because if it is angle CXY then angle AXY and CXY would meet at the point X itself.
The locus of the point P will be a straight line.
Use the link below:
click on the play button on the bottom left corner of the screen…
NOTE: In the question angle CXY should be angle CYX because if it is angle CXY then angle AXY and CXY would meet at the point X itself.
The locus of the point P will be a straight line.
Use the link below:
click on the play button on the bottom left corner of the screen...
Let ABCD be the quadrilateral
Given: BA + DA + CA = AB + CB + DB = AC + BC + DC = AD + BD + CD
To prove: quadrilateral ABCD is a rectangle
Solution:
As we know: BA + DA + CA = AC + BC + DC
We get: BA - BC = DC - DA --- (i)
Similarly from, AB + CB + DB = AD + BD + CD
We get: CB - CD = AD - AB --- (ii)
By adding (i) & (ii) we get,
BA - BC + CB - CD = DC - DA + AD - AB
BA - CD = DC - AB
2*AB = 2*CD
AB = CD
Similarly we can prove for: BC = AD
We have have proved that quadrilateral ABCD is a PARALLELOGRAM...
Now to prove that quadrilateral ABCD is indeed a rectangle. We have to prove that the the diagonals of the quadrilateral are equal... So, for quadrilateral ABCD we have to prove AC = BD
As we know: BA + DA + CA = AB + CB + DB
AC = BD (because, CB = DA)
We have proved that the opposite sides and the diagonals are equal...
Hence, quadrilateral ABCD is a RECTANGLE...
