Schooling · Class 7 · Mathematics · Constructions and Tilings · Chapter on a page
CBSE Class 7 · Mathematics · NCERT Ganita Prakash-II
Constructions and Tilings: chapter on a page
A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).
About the notes: Written by Shishya's AI on 26 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.
Fact-checked on 21 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain.
Mind map
Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.
The mind map as a list
- Key ideas
- A compass is used to draw arcs and…
- To bisect means to divide into two…
- A perpendicular bisector of a line…
- To construct a triangle, you need at…
- A tiling (tessellation) covers a…
- Regular polygons that can tile a…
- The sum of angles meeting at each…
- Formulas and facts
- Sum of angles in a triangle = 180°
- Sum of angles around a point = 360°
- Interior angle of a regular polygon…
- Equilateral triangle interior angle…
- Square interior angle = 90°. Four of…
- Regular hexagon interior angle =…
- Regular pentagon interior angle =…
- Watch out for
- Changing the compass width while…
- Drawing arcs that are too small to…
- Forgetting that angles at a meeting…
- Trying to tile with regular…
- Measuring with a ruler instead of…
What this chapter is about
This chapter teaches you how to use a ruler and compass to construct geometric shapes accurately. You will learn to draw angles of specific sizes, bisect angles and line segments, and construct triangles when certain measurements are given. These skills help you create exact figures without guessing or measuring repeatedly.
Key ideas
- A compass is used to draw arcs and circles of exact radius. A ruler (or straightedge) draws straight lines. Together, they let you construct precise figures.
- To bisect means to divide into two equal parts. You can bisect a line segment or an angle using arcs drawn with a compass.
- A perpendicular bisector of a line segment is a line that cuts it into two equal halves at a right angle (90°).
- To construct a triangle, you need at least three pieces of information, such as three sides (SSS), two sides and the included angle (SAS), or two angles and the included side (ASA).
- A tiling (tessellation) covers a flat surface using one or more shapes with no gaps and no overlaps.
- Regular polygons that can tile a plane by themselves are equilateral triangles, squares, and regular hexagons. Regular pentagons cannot tile a plane alone.
- The sum of angles meeting at each point in a tiling must be exactly 360°.
Formulas and facts to remember
- Sum of angles in a triangle = 180°.
- Sum of angles around a point = 360°.
- Interior angle of a regular polygon with n sides = (n − 2) × 180° ÷ n.
- Equilateral triangle interior angle = 60°. Six of them meet at a point: 6 × 60° = 360°.
- Square interior angle = 90°. Four of them meet at a point: 4 × 90° = 360°.
- Regular hexagon interior angle = 120°. Three of them meet at a point: 3 × 120° = 360°.
- Regular pentagon interior angle = 108°. This does not divide 360° evenly, so pentagons alone cannot tile a plane.
Common mistakes
- Changing the compass width while drawing arcs for a bisector → Keep the compass opening fixed throughout that step.
- Drawing arcs that are too small to intersect → Open the compass to more than half the segment length.
- Forgetting that angles at a meeting point must total 360° → Always check the angle sum when planning a tiling.
- Trying to tile with regular pentagons and expecting no gaps → Remember that 108° does not divide 360° evenly; pentagons leave gaps.
- Measuring with a ruler instead of constructing with compass arcs → Constructions require arcs; measuring defeats the purpose.
Quick revision
- Bisect means divide into two equal parts using compass arcs.
- Perpendicular bisector: cuts a segment at its midpoint at 90°.
- SSS, SAS, and ASA are the common ways to construct a triangle.
- Among regular polygons, only equilateral triangles, squares, and regular hexagons tile a plane by themselves.
- Angles around any point in a tiling must add up to 360°.