Q. 5

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

Answer :

The steps of the required construction are:

1) Draw a line segment and choosing an arbitrary point A on it as the center and with any radius, draw a semi-circle, intersecting the line segment at point B and C. Choosing any arbitrary point D on the semi-circle, join AD. Thus, BAD and CAD are a linear pair of angles.



2) Taking B as the center draw an arc of any radius greater than . Now, Taking D as the center and the keeping the same radius, draw another arc, intersecting the previous arc at E. Join AE. Similarly, Taking C as the center draw an arc of any radius greater than . Now, Taking D as the center and the keeping the same radius, draw another arc, intersecting the previous arc at F. Join AF.



3) AE and AF are angle bisectors of BAD and CAD respectively. Measure FAE using a protractor. It comes out to be 90°.

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