Perpendicular and Angle Bisectors

Perpendicular and Angle Bisectors

Let's review!

Perpendicular Bisector

A line, segment, or ray that divides a line segment in half at 90 degree angles.

Perpendicular Bisector Theorem

If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

Multiple Choice

Can you use the Perpendicular Bisector Theorem on this image?

• Yes

• No

Fill in the Blanks

Suppose line m is the perpendicular bisector of  $\overline{AB}$  . Find the value of x. 

Converse of the Perpendicular Bisector Theorem

If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.

Fill in the Blanks

In the diagram,

 $\overline{AD}$  is the perpendicular bisector of  $\overline{BC}$  . Find the value of x.

Fill in the Blanks

In the diagram,

 $\overline{AD}$  is the perpendicular bisector of  $\overline{BC}$  . Find the value of  $\overline{BD}$  

Angle Bisector Theorem

If a point is on the bisector of an angle, then it is equidistant from the sides of the angle.

Fill in the Blanks

Find the value of x.

Converse of the Angle Bisector Theorem

If a point in the interior of an angle is equidistant from the sides of the angle, then it is on the bisector of the angle.

Fill in the Blanks

Find the value of x.