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

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.

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 =  =  = 6 [Substitute AB = 12.]
Step 4: AO = OB = 6 cm

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