Revision Notes for Class 7 Maths Chapter 14: Constructions and Tilings

Quick revision notes summarising all key concepts from Class 7 Maths Chapter 14 “Constructions and Tilings” (ruler-and-compass constructions and tiling). These Class 7 Mathematics Chapter 14 notes are ideal for quick revision just before exams.

Last Updated: September 23, 2026

• Perpendicular bisector: the set of all points equidistant from two given points. Constructed using equal-radius arcs from each endpoint (each individual arc-pair must share one radius, but the two pairs of arcs — above and below, or both on one side — need not use the same radius as each other).
• 3-4-5 rope method: since 3² + 4² = 5², a triangle with sides in the ratio 3:4:5 always has a right angle opposite its longest side — an ancient (Sulba-Sutra) way to construct a 90° angle without instruments.
• Angle bisector: constructed using an arc from the vertex cutting both arms, then equal-radius arcs from those two points meeting at a new point; joining the vertex to that point bisects the angle (proved via SSS congruence).
• Repeated bisection of a 90° angle gives 45°, 22.5°, and so on; sums of constructible angles give more constructible angles — but not every angle (e.g. 65.5°) is reachable this way.
• Copying an angle or figure: use a compass to transfer chord lengths (not a protractor) between the original and the copy, recreating identical angles via SSS congruence.
• Constructing a parallel line: copy the angle a transversal makes with a given line onto a new point — equal corresponding angles guarantee the lines are parallel.
• Regular hexagon in a circle: stepping off the circle’s own radius as a chord six times around the circumference always returns to the start exactly, since each step subtends a 60° central angle (6 × 60° = 360°).
• Constructing a perpendicular through an external point P: draw an arc centred at P cutting the line at two points; P is equidistant from those points, so it lies on their perpendicular bisector — constructing that bisector gives the required perpendicular through P.
• Tangram: a 7-piece puzzle (2 large + 1 medium + 2 small right triangles, 1 square, 1 parallelogram) where all 7 pieces must be used edge-to-edge, without gaps or overlaps, to form new figures.
• Checkerboard tiling-impossibility argument: every 2×1 domino tile covers exactly one black and one white square on a checkerboard-coloured region. If a region has an unequal number of black and white squares, it can never be completely tiled by such dominoes — a rigorous proof technique, not just a rule of thumb.

See also: NCERT Solutions for Class 7 Maths Chapter 14

Practice more: Extra Questions for Class 7 Maths Chapter 14

For the full chapter, see the Class 7 Maths Formulas Handbook.

Frequently Asked Questions

What basic tools are used for accurate geometric constructions in this chapter?
Accurate constructions are done using only a ruler for drawing straight lines of measured length and a compass for drawing arcs and circles of a fixed radius, without relying on a protractor.

What makes a set of shapes suitable for tiling a flat surface without any gaps or overlaps?
Shapes are suitable for tiling, or tessellation, when copies of them can be arranged so their angles fit exactly around every point, commonly seen with equilateral triangles, squares, and regular hexagons.

Written by Satish

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