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Chapter Summary

Constructions (Using Ruler and Compass only)

ICSE · Class 8 · Mathematics

Summary of Constructions (Using Ruler and Compass only) for ICSE Class 8 Mathematics. Key concepts, important points, and chapter overview.

104 questions40 flashcards5 concepts

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Overview

Geometrical construction is the accurate drawing of angles, line segments, quadrilaterals, parallelograms, rectangles, rhombuses, and squares using only a ruler and a compass. The chapter focuses on exact construction steps, useful properties of shapes, and the correct use of arcs, equal radii, perp

Key Concepts

An arc is drawn from

An arc is drawn from the vertex of the given angle to cut its arms, and the same radius is used to recreate the arc on a new line segment. The distanc

An arc from the vertex cuts

An arc from the vertex cuts both arms of the angle, and equal arcs from those cut points meet at a new point. Joining the vertex to that point gives t

A 60° angle is constructed directly

A 60° angle is constructed directly by drawing two equal-radius arcs from consecutive points on a line. It is not made by bisecting another angle.

A 30° angle is obtained by

A 30° angle is obtained by bisecting a 60° angle. The relation used is ∠PBC = 1/2 ∠ABC = 1/2 × 60° = 30°.

A right angle is constructed directly

A right angle is constructed directly using arc intersections and a line through the vertex. The result is ∠ABC = 90°, so AB and BC are perpendicular.

Learning Objectives

  • Construct an angle equal to a given angle.
  • Construct angles of 60°, 30°, 90°, and 45°.
  • Construct the bisector of an angle.
  • Construct the bisector and perpendicular bisector of a line segment.
  • Construct a perpendicular to a line at a point on it and from an external point.

Frequently Asked Questions

What are the important topics in Constructions (Using Ruler and Compass only) for ICSE Class 8 Mathematics?
Constructions (Using Ruler and Compass only) covers several key topics that are frequently asked in ICSE Class 8 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Constructions (Using Ruler and Compass only) — ICSE Class 8 Mathematics?
Understand the core concepts first, then work through the 104 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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