Question

prove that the bisectors of angles of a linear pair at right angles

Answer 1

LINEAR PAIR AXIOM:Sum of adjacent angles in a line is 180°.
bisector of straight angle =180°÷2=90°

 Thus,bisectors of angles of a linear pair are at right angles.

Answer 2

Given: BE bisects CBD

          BF bisects ABD

To prove: FBE=90

Proof: ABE+CBD= 180 (Linear Pair)

         2 FBD+ 2 DBE=180 (because BE bisects CBD and bf bisects ABD)

         2(FBD+DBE)= 180

         FBD+DBE=180/2=90

         FBE=90