PDF chapter test

To know clearly about the perpendicular bisectors, we should understand what perpendiculars and bisectors are.

Perpendicular lines:
When two lines or line segments meet at $$90$$ degrees, they are called perpendicular lines.

In the figure given above, the $$\overline{AB}$$ and $$\overline{MN}$$ meet each other at $$90$$ degrees at $$R$$.

In other words, $$\overline{AR}$$ doesn't need to be equal to $$\overline{RB}$$.

Bisector:
A line that divides another line into two halves is a bisector.

In the figure given above, $$\overline{MN}$$ bisects $$\overline{AB}$$ at $$R$$.

Therefore, $$AR = RB$$.

A perpendicular bisector:
A line or a line segment being both perpendicular and acting as a bisector is a perpendicular bisector.

In the figure given above, $$\overline{MN}$$ is perpendicular to $$\overline{AB}$$, and it also bisects $$\overline{AB}$$.

Thus, $$\overline{MN}$$ is the perpendicular bisector of $$\overline{AB}$$.

Therefore, $$AR = RB$$.