MathematicsState whether the following statement is true or false:The bisectors of angles of a parallelogram form a rectangle.

State whether the following statement is true or false:


The bisectors of angles of a parallelogram form a rectangle.


  1. A
    True
  2. B
    False 

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    Solution:

    Given, a parallelogram.
    In ΔADS   ,
    DAS+ADS= 1 2 A+ 1 2 D   [AS and DS are angle bisectors.]
    DAS+ADS= 1 2 A+D  
    DAS+ADS= 1 2 180 °  [As A   and D  are adjacent angles of a parallelogram.]
    DAS+ADS= 90 °  
    In ΔADS  ,
    DAS+ADS+DSA= 180 °  [By angle sum property of triangle.]
    DSA+ 90 ° = 180 °  [Proved above]
    DSA= 90 °   Similarly, APB or SPQ= 90 °   and SRQ=RQP= 90 °   Thus, PQRS is a rectangle as its internal angle is 90 °  .
    Hence, the given statement is true.
     
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