Question

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 $\overline{OA}$ and $\overline{OB}$. Let them meet at P. Is PA = PB?

Answer 1

A perpendicular bisector of a line segment is a line segment perpendicular to and passing through the midpoint of the line segment.

Steps of construction:
(i) Draw any angle with vertex O.
(ii) Take a point A on one of its arms and B on another such that OA = OB.
(iii) Draw perpendicular bisector $\overline{OA}$ and $\overline{OB}$ by drawing arcs from the points O , A and B as the centre points.
(iv) Let them meet at P. Join PA and PB.
(v) Checking the length of PA and PB by compass, we note that their lengths are equal.
OA‾\overline{OA}