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

Answer:

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Question

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

Solution

Steps of construction :

(i) Draw a linear pair

∠

D

C

A

a

n

d

∠

D

C

B

1. .

(ii) Draw the bisector of

∠

D

C

A

a

n

d

∠

D

C

B

.

(iii) With centre C and any radius, draw an arc which intersects CB at P, CD at Q and AC at R.

(iv) With centres P and Q and any radius draw two arcs which intersects at H and Join CH.

(v) With centre R and Q, any radius draw two arcs, which intersect each other at G and join CG.

Now,

∠

E

C

F

is equal to

90

∘

.

Verification :

∵

∠

D

C

A

+

∠

D

C

B

=

180

∘

⇒

1

2

∠

D

C

A

+

1

2

D

C

B

=

180

∘

×

1

2

=

90

∘

∠

E

C

F

=

90

∘

i.e. EC and FC are perpendicular to each other.