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

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Solution

Steps of construction :

(i) Draw a linear pair $∠ D C A a n d ∠ D C B .$

(ii) Draw the bisector of $∠ D C A a n d ∠ D C B .$ Now, $∠ E C F$ is equal to $90^{\circ}$ .

Verification : $∵ ∠ D C A + ∠ D C B = 180^{\circ}$

$\Rightarrow \frac{1}{2} ∠ D C A + \frac{1}{2} D C B = 180^{\circ} \times \frac{1}{2} = 90^{\circ}$

$∠ E C F = 90^{\circ}$

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

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

Steps of construction : (i) Draw a linear pair ∠DCA and ∠DCB. (ii) Draw the bisector of ∠DCA and ∠DCB. Now, ∠ECF is equal to 90∘. Verification : ∵∠DCA+∠DCB=180∘ ⇒ 12∠DCA+12DCB=180∘×12=90∘ ∠ECF=90∘ i.e. EC and FC are perpendicular to each other.