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

To do:

We have to draw a linear pair of angles, bisect each of the two angles and verify that the two bisecting rays are perpendicular to each other.

Solution:

Steps of construction:

(i) Draw a linear pair, $\angle DCA$ and $\angle DCB$.

(ii) Draw the bisectors of $\angle DCA$ and $\angle DCB$ forming $\angle ECF$ on measuring, we get, $\angle ECF = 90^o$.

Verification:

$\angle DCA +\angle DCB = 180^o$

$\frac{1}{2}\angle ∠DCA + \frac{1}{2}\angle DCB = 180^o \times \frac{1}{2}$

$= 90^o$

Therefore,

$\angle ECF = 90^o$

This implies,

$EC$ and $FC$ are perpendicular to each other.

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Updated on: 10-Oct-2022

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