Question

If ABCD is a parellogram , then show that the bisectors of any two adjacent angles of the parellogram are at right angles.

Answer 1

let  ABCD BE THE  llgm

we know that 

ANGLE A + ANGLE B = 180 DEGREE 

THEREFORE 

1/2 A + 1/2 B = 90 DEGREE  -(1)

AND WE KNOW THAT

IN TRIANGLE AOB

ANGLE BAO + ANGLE ABO +  ANGLE AOB = 180 (ANGLE SUM PROPERTY)

=> 1/2 A + 1/2 B + AOB = 180

=> AOB = 180 -( 1/2 A + 1/2 B)

=> AOB = 180 - 90  (FROM 1)

=> AOB = 90  => ANGLE BISECTOR OF 2 ADJ. ANGLES INTERSECT AT 90

HENCE PROOVED

Hope This helps :)