Answer:
Step-by-step explanation:
Let OP be perpendicular bisector of MN
Perpendicular:
We say two lines are perpendicular to each other if they intersect at right angle.
If OP is perpendicular to MN at point say K , it means \(\angle OKN=90^{\circ}\)
Bisector:
A line is said to be a bisector of another line if it intersects that line at it's midpoint .
If OP bisects MN at point K, it means MK=KN
Two line segments are said to be congruent if they are of same length.
Join OM and ON
Consider \(\Delta OKM \,,\,\Delta OKN\)
OK=OK (common side)
MK=KN (OP bisects MN)
\(\angle OKM =\angle OKN\) \(\left ( OP\perp MN \right )\)
Therefore, ΔOKM≅ΔOKN ( by SAS congruence condition )
So, OM=ON ( corresponding sides of congruent triangles )
