Exploring Perpendicular and Angle Bisectors in Geometry

What does the perpendicular bisector theorem state?

• A point on the angle bisector of an angle is equidistant from the sides of the angle.

• A point on the perpendicular bisector of a segment is closer to one endpoint than the other.

• A point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment.

• A point on the angle bisector of an angle is closer to one side than the other.

If point A is on the perpendicular bisector of line segment BC and AC is 9 units, what is the length of AB?

• 12 units

• 4.5 units

• 9 units

• 18 units

If point F is on the perpendicular bisector of line segment GE and EH is 3 units, what is the length of EG?

• 6 units

• 3 units

• 9 units

• 7 units

Given that R is on the perpendicular bisector of line segment ST and the lengths of RS and RT are equal, if 2x + 2 = 3x, what is the value of x?

• 2

• 1

• 4

• 3

What does the angle bisector theorem state?

• A point on the perpendicular bisector of a segment is closer to one endpoint than the other.

• A point on the angle bisector of an angle is closer to one side than the other.

• A point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment.

• A point on the angle bisector of an angle is equidistant from the sides of the angle.

If point D is on the angle bisector of angle CAB and angle DAB is 20 degrees, what is the measure of angle CAD?

• 30 degrees

• 20 degrees

• 10 degrees

• 40 degrees

If point D is on the angle bisector of angle CAB and the distance from D to B is 5 units, what is the distance from D to C?

• 10 units

• 7 units

• 5 units

• 2.5 units

Given that point D is on the angle bisector of angle BAC and the lengths of DB and DC are equal, if 3x + 1 = 5x - 1, what is the value of x?

• 4

• 3

• 2

• 1

If point D is on the angle bisector of angle BAC and x = 1, what is the length of BD if BD = 3x + 1?

• 2

• 3

• 5

• 4

If point D is on the angle bisector of angle BAC and the lengths of DB and DC are equal, what equation can be set up to find x if BD = 3x + 1 and DC = 5x - 1?

• 3x + 1 = 5x - 1

• 3x - 1 = 5x - 1

• 3x + 1 = 5x + 1

• 3x - 1 = 5x + 1