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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