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.

• 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.

Written by Satish

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