Exploring Perpendicular and Angle Bisectors

If two students are positioned on either side of the room with the teacher in between, what direction should the teacher walk to remain equidistant from both students?

• Towards student A

• In a circular path around the students

• Towards student B

• On a line that is the perpendicular bisector of the line segment between the students

What property allows us to say that segment CD is congruent to itself?

• Substitution Property

• Transitive Property

• Reflexive Property

• Symmetric Property

Which congruence postulate is used to prove that triangle ACD is congruent to triangle BDC?

• Side-Angle-Side (SAS)

• Angle-Angle-Side (AAS)

• Side-Side-Side (SSS)

• Angle-Side-Angle (ASA)

Given PS = 8 and QT = 6, what is the length of PQ if M is the perpendicular bisector?

• 8

• 12

• 10

• 14

If PS = 3x and QS = x + 10, and M is the perpendicular bisector, what is the value of QS?

• 10

• 25

• 20

• 15

According to the perpendicular bisector converse theorem, if a point is equidistant from the endpoints of a segment, where does it lie?

• On the perpendicular bisector of the segment

• At one of the endpoints

• On the segment itself

• Anywhere on the plane

What does the angle bisector theorem state about a point on the bisector of an angle?

• It lies on the perpendicular bisector of the angle

• It is equidistant from the two sides of the angle

• It is closer to one side of the angle

• It forms a right angle with the bisector

If BD bisects angle ABC and CD = 20, what is the length of AD?

• 15

• 10

• 20

• 25

Given DA is congruent to DC, and the measures of angles DBC and DBA are 4y + 7 and 2y + 16 respectively, what is the measure of angle DBC?

• 30

• 25

• 20

• 35

What is the equation of the perpendicular bisector of the segment with endpoints (-1, 6) and (3, 4) in point-slope form?

• y - 5 = 2(x - 1)

• y - 5 = -2(x - 1)

• y - 5 = 1/2(x - 1)

• y - 5 = -1/2(x - 1)