Concurrent Lines — Chapter Summary
NIOS · Class 10 · Maths
Summary of Concurrent Lines for NIOS Class 10 Maths. Key concepts: Three or more lines that meet, A triangle has three angle and A triangle has three.
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Overview
Concurrent lines are lines in a plane that meet at one common point. In triangle geometry, four important sets of lines are studied: angle bisectors, perpendicular bisectors, altitudes, and medians. Each set has a special point of concurrency. These points are the incentre, circumcentre, orthocentre
Key Concepts
Three or more lines that meet
Three or more lines that meet at exactly one point are called concurrent lines. The common point is the point of concurrency.
A triangle has three angle bisectors
A triangle has three angle bisectors. They are concurrent at the incentre I. The incentre is equidistant from all three sides, so IL = IM = IN. A circ
A triangle has three perpendicular bisectors
A triangle has three perpendicular bisectors. They are concurrent at the circumcentre O. The circumcentre is equidistant from all three vertices, so A
An altitude is a perpendicular drawn
An altitude is a perpendicular drawn from a vertex to the opposite side. The three altitudes of a triangle are concurrent at the orthocentre H.
A median joins a vertex
A median joins a vertex to the midpoint of the opposite side. The three medians are concurrent at the centroid G. The centroid divides each median in
Learning Objectives
- Understand the meaning of concurrent lines and point of concurrency
- Identify the angle bisectors, perpendicular bisectors, altitudes, and medians of a triangle
- Learn the special points formed by these lines: incentre, circumcentre, orthocentre, and centroid
- Use key properties such as equal distances, ratio 2:1, and special positions in different triangles
- Apply the results to equilateral and isosceles triangles
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