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Revision Notes

Constructions (Using Ruler and Compass only)

ICSE · Class 8 · Mathematics

Quick revision notes for Constructions (Using Ruler and Compass only) — ICSE Class 8 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

104 questions40 flashcards5 concepts

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Key Topics to Revise

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1. Angle Construction Basics

  • An angle equal to a given angle is constructed by copying the opening of the given angle using equal arcs and a transferred distance between arc-cut points.
  • A 60° angle is constructed directly with two equal-radius arcs, not by bisecting another angle.
  • A 30° angle is obtained by bisecting a 60° angle.
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2. Bisector of an Angle and of a Line Segment

  • The bisector of an angle is drawn by taking equal arcs from the two points where the first arc cuts the arms of the angle.
  • The radius used to find the intersection point O when bisecting an angle must be more than half the distance between the two arc-cut points D and E.
  • The bisector of a line segment can be constructed by two methods.
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3. Perpendiculars and Parallels

  • A perpendicular can be drawn at a point on a line by using equal arcs from two points on the line and their intersection.
  • A perpendicular can also be drawn from an external point to a line by using arcs from two points on the line and joining the external point to the intersection point.
  • When constructing a perpendicular at a point on a line, the radius for the second pair of arcs from C and D must be more than half the distance between C and D.
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4. Quadrilateral Constructions

  • Five separate quadrilateral construction cases are given: four sides and one angle; three consecutive sides and two included angles; four sides and one diagonal; three sides and two diagonals; two adj
  • In the four-sides-and-one-diagonal case, the diagonal itself is used as a radius from one vertex to locate another vertex.
  • Each case uses a different starting set of known measurements.

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Full Notes

Key Concepts

An arc is drawn fromAn arc from the vertex cutsA 60° angle is constructed directlyA 30° angle is obtained byA right angle is constructed directly

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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