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Mathematics · Class 9 · Chapter 11: Line Bisectors and Angle Bisectors

8 min

Key points

Perpendicular bisector of a line segment is a line perpendicular to the segment and passing through its midpoint
Every point on the perpendicular bisector of a line segment is equidistant from the endpoints of the segment
Angle bisector divides an angle into two equal parts
Every point on the bisector of an angle is equidistant from the arms of the angle
The perpendicular from any point on angle bisector to the arms of the angle are equal
Three angle bisectors of a triangle meet at a point called incenter
The incenter is equidistant from all three sides of the triangle
Perpendicular bisectors of the sides of a triangle meet at a point called circumcenter

Definitions

Perpendicular Bisector: A line which is perpendicular to a line segment and passes through its midpoint is called perpendicular bisector of the line segment.
Angle Bisector: A ray which divides an angle into two equal angles is called angle bisector.
Incenter: The point of intersection of the three angle bisectors of a triangle is called incenter.
Circumcenter: The point of intersection of the perpendicular bisectors of the sides of a triangle is called circumcenter.
Equidistant: A point is said to be equidistant from two points if its distance from both points is equal.

Worked example

Define perpendicular bisector of a line segment. Construct the perpendicular bisector of line segment AB = 6 cm. (6 marks)

Perpendicular bisector is a line passing through midpoint of line segment and perpendicular to it. Construction completed showing PQ ⊥ AB at midpoint M.

Common mistakes

Students confuse incenter with circumcenter - remember incenter is for angle bisectors
Forgetting to mark right angles in perpendicular bisector diagrams
Not stating 'given' and 'to prove' clearly in geometry proofs
Confusing equidistant from sides vs equidistant from vertices
Drawing angle bisector incorrectly - it should divide angle into exactly equal parts

Quick recap

Perpendicular bisector passes through midpoint and is perpendicular to line segment. Angle bisector divides angle into two equal parts. Any point on perpendicular bisector is equidistant from endpoints. Construction uses compass arcs with radius greater than half the segment length.

Generated by AI from Sindh Textbook Board material; review state: ai_unreviewed. MCQs, past-paper references and examiner notes are held back until a teacher has checked them.