Name: Construction of Angles Using Protractor
Uploaded: 2019-07-19
Duration: 4 min 7 s
Description: We know that an angle is formed when two rays join at a common point. In this video session, learn how to construct angles using a basic geometry tool called a protractor.

Question

Draw a pair of vertically opposite angles. Bisect each of the two angles. Verify that the bisecting rays are in the same line.

Accepted Answer

Steps of construction:

Draw two lines $A B$ and $C D$ intersecting each other at $O$ .We know that the vertically opposite angles are equal.
$∴ ∠ B O C = ∠ A O D$

and $∠ A O C = ∠ B O D$

We bisect angle $A O C$ and draw the bisecting ray as $O X$ .

Similarly, we bisect angle $B O D$ and draw the bisecting ray as $O Y$ .

Now,

$∠ X O A + ∠ A O D + ∠ D O Y$

$= \frac{1}{2} ∠ A O C + ∠ A O D + \frac{1}{2} ∠ B O D$

$= \frac{1}{2} ∠ B O D + ∠ A O D + \frac{1}{2} ∠ B O D [As, ∠ A O C = ∠ B O D]$

$= ∠ A O D + ∠ B O D$

$∵ A B$ is a line.
$∴ ∠ A O D$ and $∠ B O D$ are supplementary angles and the sum of these two angles will be $180 °$ .
$∴ ∠ X O A + ∠ A O D + ∠ D O Y = 180 °$
We know that the angles on one side of a straight line will always add to $180 °$ .
Also, the sum of the angles is $180 °$ .
$∴ X Y$ is a straight line.
Thus, $O X$ and $O Y$ are in the same line.

Draw a pair of vertically opposite angles. Bisect each of the two angles. Verify that the bisecting rays are in the same line.

Important Questions on Geometrical Constructions

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