Draw any angle with vertex O. Take a point A on one of its arms and B on another such that OA = OB. Draw the perpendicular bisectors of OA and OB. Let them meet at P. Is PA = PB?

Solution:

We can construct an angle bisector by following the steps below.

Step 1: Draw an angle with vertex as O.

Step 2: Take O as center make two arcs on both rays of this angle. Mark these points as A and B.

Step 3: By taking O and A as centers and with a radius, more than half of OA, draw two arcs on both the sides of OA and mark the points as C and D where the arcs intersect each other.

Step 4: Join CD to construct a perpendicular bisector of OA.

Step 5: By taking O and B as centers and with a radius of more than half of OB, draw two arcs on both sides of OB and mark the points as E and F where the arcs intersect each other.

Step 6: Join EF to construct a perpendicular bisector of OB.

The perpendicular bisectors CD and EF intersect each other at point P.

On measuring we see that, PA = PB.

Class 6 Maths NCERT Solutions Chapter 14 Exercise 14.5 Question 9

Draw any angle with vertex O. Take a point A on one of its arms and B on another such that OA = OB. Draw the perpendicular bisectors of OA and OB. Let them meet at P. Is PA = PB?

Summary:

The perpendicular bisectors CD and EF of OA and OB respectively intersect each other at point P. On measuring we see that, PA = PB.

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