Exploring Perpendicular and Angle Bisectors

What is the goal of the lesson on perpendicular and angle bisectors?

• To understand the properties of parallel lines

• To learn about congruent triangles

• To study the properties of circles

• To use properties of perpendicular bisectors and angle bisectors

In the diagram, if line CD is the perpendicular bisector of line segment AB, which of the following is true?

• Line segment CD is congruent to line segment AB

• Line segment AD is congruent to line segment CA

• Line segment CA is congruent to line segment AB

• Line segment AD is congruent to line segment DB

According to the perpendicular bisector theorem, if a point is on the perpendicular bisector of a segment, it is:

• Always at the midpoint of the segment

• Not related to the endpoints

• Equidistant from the endpoints of the segment

• Closer to one endpoint than the other

What does the converse of the perpendicular bisector theorem state?

• If a point is on the angle bisector, it is equidistant from the sides of the angle

• If a point is on the perpendicular bisector, it is equidistant from the endpoints

• If a point is equidistant from the sides of an angle, it lies on the angle bisector

• If a point is equidistant from two endpoints, it lies on the perpendicular bisector

If angle BCD measures 132 degrees, what is the measure of angle C?

• 90 degrees

• 66 degrees

• 45 degrees

• 132 degrees

If line TR is a perpendicular bisector and TU is 85, what is the length of ST?

• 42.5

• 58

• 170

• 85

Given QT is congruent to ST and RS equals 56, what is the length of QR?

• 84

• 28

• 112

• 56

Using the angle bisector theorem, if two sides are congruent and form right angles, what is the measure of angle FHG?

• 45 degrees

• 90 degrees

• 55 degrees

• 60 degrees

If line HJ is a perpendicular bisector and the sides are equal, what is the value of P if 2P equals 24?

• 18

• 6

• 24

• 12

If UV and UX are both 34, and WV equals 5P and WX equals P plus 48, what is the value of P?

• 8

• 6

• 12

• 10