Perpendicular Bisector Theorem

Front

What is the Perpendicular Bisector Theorem?

Back

The Perpendicular Bisector Theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

Front

If point P is on the perpendicular bisector of segment AB, what can we say about the distances PA and PB?

Back

PA = PB; point P is equidistant from points A and B.

Front

Solve for x: If AB = 10 and AP = x, PB = 10 - x, what is x?

Back

x = 5.

Front

What does it mean for a line to be a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a 90-degree angle.

Front

If AD is a perpendicular bisector of segment BC, what can we conclude about segments AB and AC?

Back

AB = AC; point D is equidistant from points B and C.

Front

Find the length of segment PQ if P(2, 3) and Q(2, 8).

Back

Length of PQ = 5.

Front

What is the relationship between the angles formed by a perpendicular bisector and the segments it bisects?

Back

The angles formed are right angles (90 degrees).

Front

If the coordinates of points A and B are A(1, 2) and B(1, 6), what is the midpoint M of segment AB?

Back

Midpoint M = (1, 4).

Front

True or False: The perpendicular bisector of a segment can be a segment itself.

Back

False; it is a line that extends infinitely in both directions.

Front

If angle A measures 75°, what is the measure of angle B if AB is the perpendicular bisector of segment CD?

Back

Angle B = 75°; angles A and B are congruent.