Question

Given that OP is the perpendicular bisector of MN, which segments are congruent?

Answer 1

whats the options...

Answer 2

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 )