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Syllabus

Constructions — Syllabus

NIOS · Class 10 · Maths

What Constructions covers in NIOS Class 10 Maths: 4 topics, for the 2026-27 session. Part of the NIOS Class 10 Maths syllabus.

43 questions24 flashcards3 formulas & key relations5 concepts

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A step-by-step diagram illustrating the construction of dividing a line segment AB internally in a given ratio (e.g., 2:3) using a ray and parallel lines. Shows the initial line segment, the acute ang
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4 Topics · NIOS Class 10 Maths · 2026-27

Topics in Constructions

1

1. Division of a Line Segment in a Given Ratio

  • A line segment can be divided internally in a given ratio by using a ray, equal divisions on the ray, and a parallel line.
  • For ratio 2 : 3, the total number of equal points marked on the auxiliary ray is 5.
  • The point on the segment is obtained by drawing a line through the correct marked point parallel to the line joining the last marked point to the other end of the segment.
2

2. Construction of Triangles

  • A triangle can be constructed when enough data is given to fix it uniquely.
  • The main construction types are SSS, SAS, ASA, RHS, perimeter with base angles, sum of two sides, difference of two sides, and two sides with a median.
  • In SSS, all three sides are given.
3

3. Similar Triangles by Scale Factor

  • A triangle similar to a given triangle can be constructed using a scale factor.
  • Scale factor means the ratio of the sides of the new triangle to the corresponding sides of the given triangle.
  • For scale factor 3/5, 5 equal points are marked on the auxiliary ray.
4

4. Tangents to a Circle

  • A tangent to a circle at a point on the circle is perpendicular to the radius at that point.
  • To draw a tangent at a point on the circle, join the centre to the point and draw a perpendicular at that point.
  • To draw tangents from an external point, join the point to the centre, bisect that segment, and draw an auxiliary circle.

Key Concepts

Central concept: Geometrical construction with ruler and compasses

Division of a line segment in a given ratioTriangle construction from given dataSimilar triangle constructionTangents to a circle

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Frequently Asked Questions

What are the important topics in Constructions for NIOS Class 10 Maths?
Key topics in Constructions include Division of a Line Segment in a Given Ratio, Construction of Triangles, Similar Triangles by Scale Factor, Tangents to a Circle. Study these first, then practise questions on each for the NIOS Class 10 board exam.
How should I revise Constructions for the NIOS Class 10 board exam?
Learn the core ideas first, then work through the 43 practice questions on Constructions. Revise 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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All NIOS Class 10 Maths Syllabus

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