Perpendicular Bisector

Definition of Perpendicular Bisector

Perpendicular Bisector is a perpendicular line or a segment that passes through the midpoint of a line.

More About Perpendicular Bisector

  • A perpendicular bisector divides a line segment into two equal segments.
  • The intersecting point of the three perpendicular bisectors of a triangle is called circumcenter.

Examples of Perpendicular Bisector

    Examples of  Perpendicular Bisector
    In the figure shown, AB is the perpendicular bisector of the line segment PQ passing through its midpoint O.

Video Examples: Perpendicular Bisector of a Triangle - MathHelp.com


Solved Example on Perpendicular Bisector

Ques: AB is a line segment of length 12 cm. CD is the perpendicular bisector of AB. Find the length of AO and OB.

    Examples of  Perpendicular Bisector
    Choices:
    A. 6 cm and 8 cm
    B. 7 cm and 7 cm
    C. 6 cm and 6 cm
    D. 7 cm and 6 cm
    Correct Answer: C

Solution:

    Step 1: A perpendicular bisector divides a line segment into two equal parts.
    Step 2: The length of AB is 12 cm and CD is the perpendicular bisector of AB.
    Step 3: So, AO = OB = Examples of  Perpendicular Bisector = Examples of  Perpendicular Bisector = 6 [Substitute AB = 12.]
    Step 4: AO = OB = 6 cm