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PROVE THAT BISECTOR OF ANY TWO ADJACENT ANGLES OF PARALLELOGRAM ARE AT RIGHT ANGLES.
 

Asked by modmakers.goa 4th July 2016, 7:13 PM
Answered by Expert
Answer:
begin mathsize 12px style Let space ABCD space be space straight a space parallelogram space where space OA space and space OD space are space the space bisectors space of space adjacent space angles space straight A space and thin space straight D.
Since space ABCD space is space straight a space parallelogram comma space AB space parallel to DC. space left parenthesis Opposite space sides space of space straight a space parallelogram space are space parallel. right parenthesis
Also comma space angle BAD space plus space angle CDA space equals space 180 degree space left parenthesis Sum space of space the space interrior space angles space on space the space same space sides space of space the space transversal space is space 180 degree. right parenthesis
rightwards double arrow 1 half angle BAD space plus space 1 half angle CDA space equals space 1 half cross times 180 degree
rightwards double arrow angle 1 space plus space angle 2 space equals space 90 degree space left parenthesis AO space and space DO space are space angle space bisectors space of space angle straight A space and space angle straight D right parenthesis.. left parenthesis 1 right parenthesis
In space increment AOD comma
angle 1 space plus space angle AOD space plus space angle 2 space equals 180 degree
rightwards double arrow angle AOD space space plus 90 degree equals 180 degree.. left parenthesis from space left parenthesis 1 right parenthesis right parenthesis
rightwards double arrow angle AOD equals 180 degree space minus space 90 degree space equals space 90 degree
rightwards double arrow In space straight a space parallelogram comma space the space bisectors space of space the space adjacent space angles space intersect space at space right space angles.
end style
Answered by Expert 5th July 2016, 10:00 AM
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