Question

Draw a linear pair of angles. Bisect each of the two angles. Verify that the two bisecting rays are perpendicular to each other.

Answer 1

Since iQ & jQ are angle bisector of <A & <B respectively

=> 2<C= <A ( because iQ is bisector

of angle A)

______(1)

=> 2<D=<B ( because jQ is bisector

of angle B)

____(2)

also , <A+<B=180° (Linear pair)

from (1)&(2)

=>2<C+2<D =180°

=>2( <C+<D) =180°

=> <C+<D =90°

hence, angle subtended by iQ & jQ is 90° i.e. <c+<d

=> angle bisectors are perpendicular to each other

hence proved.

Answer 2

Step-by-step explanation:

• Here we have a straight line AB.On line AB take a point C. Draw a ray CF.

        Let

        ∠FCB = 2y

        ∠ACF = 2x

• We know that

        ∠ACF +∠FCB =180° (by linear pair angle)

         2x+2y =180°

         So

        x + y =90°        ...1)

• Now from point C draw a ray CE which bisect ∠ ACF, So

        ∠ACE =∠ ECF =x

• Similarly from point C draw a ray CD which bisect ∠FCB, So

        ∠FCD =∠DCB =y

• Where

        ∠ECD =∠ECF +∠FCD

         We can write above equation

         ∠ECD = x + y

         From equation 1), above equation can be written as

        ∠ECD = 90°  Proved