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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 -

Steps of construction :
(i) Draw a linear pair ∠DCA and ∠DCB.
(ii) Draw the bisectors of ∠DCA and ∠DCB. Forming ∠ECF on measuring we get ∠ECF = 90°.
Verification : ∵∠DCA + ∠DCB = 180°
  ∠DCA +  ∠DCB = 180° x  = 90°
∴ ∠ECF = 90°
i.e. EC and FC are perpendicular to each other.

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