Class 9 Math Chapter 11: All Notes & Resources
Choose a resource below for Chapter 11 Loci and Construction, from solved exercises to definitions and MCQs.
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Class 9 Mathematics Chapter 11 explores the fascinating geometric concepts of loci and construction. You will learn to construct various triangles, draw perpendicular bisectors, medians, altitudes, and angle bisectors, and understand the properties of their points of concurrency. This hub gathers every Chapter 11 resource in one place. Start with the Chapter 11 definitions for quick revision, then move to the solved exercises below. For targeted practice, try the Chapter 11 MCQs. You can also review the Grade 9 Math Pairing Scheme to understand paper weightings. When you are done, return to the main Class 9 Mathematics page for the next chapter.
Last updated: October 23, 2026
Exercise 11.1 Solved
Construct triangles with given side lengths, angles, and verify the concurrency of perpendicular bisectors and medians.
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Exercise 11.2 Solved
Construct triangles and draw angle bisectors, altitudes, and their points of concurrency (incentre and orthocentre).
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Exercise 11.3 Solved
Construct loci for points at a given distance from a point or line, and find the intersection of multiple loci.
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Chapter 11 Definitions
All key definitions for loci, perpendicular bisectors, medians, altitudes, and points of concurrency.
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Chapter 11 MCQs
Multiple-choice questions covering the entire chapter with detailed solutions, perfect for exam preparation and self-testing.
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Muhammad Tayyab
Subject Specialist Math
MSc Mathematics · Govt Christian High School Daska, Sialkot, Punjab
Last updated: October 23, 2026
Key Concepts – Loci and Construction
Locus of a Point
Distance = constant
From a fixed point, the locus is a circle centered at the fixed point.
Locus from a Line
Parallel Lines
The locus of points at a constant distance from a fixed line are two parallel lines.
Locus Equidistant from 2 Points
Perpendicular Bisector
The locus of points equidistant from two fixed points is the perpendicular bisector of the line segment joining them.
Locus Equidistant from 2 Lines
Angle Bisector
The locus of points equidistant from two intersecting lines is the pair of angle bisectors.
Median
Vertex to Midpoint
A line segment joining a vertex to the midpoint of the opposite side. Intersect at the centroid.
Altitude
Vertex to Opposite Side
A perpendicular line segment from a vertex to the opposite side. Intersect at the orthocentre.
Chapter 11 Frequently Asked Questions
What is a locus?
A locus is a set of points that satisfy a specific geometric condition. For example, the locus of points at a fixed distance from a given point is a circle.
What is the point of concurrency?
The point of concurrency is the single point where three or more lines, rays, or line segments intersect. In a triangle, the medians intersect at the centroid, altitudes at the orthocentre, and perpendicular bisectors at the circumcentre.
What is a median of a triangle?
A median is a line segment that connects a vertex of the triangle to the midpoint of the opposite side. All three medians of a triangle intersect at a single point called the centroid.
What is an altitude of a triangle?
An altitude is a perpendicular line segment drawn from a vertex to the line containing the opposite side. The three altitudes of a triangle intersect at the orthocentre.
What is the triangle inequality theorem?
The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This is a necessary condition for a triangle to exist.
Created by Hira Science Academy | Aligned with Punjab Board 2027 Syllabus