NCERT Class 7 Maths Chapter 14
Constructions and Tilings
This chapter from Ganita Prakash Part 2 develops CBSE Class 7 students' skills in geometric constructions using a compass and ruler, and introduces the fascinating world of tessellations and tilings. Students learn to construct triangles, perpendicular bisectors, and angle bisectors, and explore which shapes tile a plane without gaps or overlaps. The chapter connects geometry to art, architecture, and nature.
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Key Terms
- Geometric Construction
- The drawing of accurate geometric figures (lines, angles, triangles) using only a compass and a straightedge (ruler without markings), without measurements.
- Perpendicular Bisector
- A line that is perpendicular to a given line segment and passes through its midpoint, dividing it into two equal halves.
- Angle Bisector
- A ray that divides an angle into two equal smaller angles. It can be constructed using a compass and straightedge.
- Tessellation
- A pattern of one or more shapes that cover a plane completely without any gaps or overlaps. Also called a tiling.
- Regular Polygon
- A polygon with all sides equal and all angles equal. Examples include equilateral triangles, squares, and regular hexagons. Only three regular polygons can tile a plane by themselves.
- Midpoint
- The point that divides a line segment into two equal halves. The perpendicular bisector of a segment passes through its midpoint.
Frequently Asked Questions
How do you construct the perpendicular bisector of a line segment?▾
To construct a perpendicular bisector: (1) Draw a line segment AB. (2) Open the compass to more than half of AB. (3) Draw arcs above and below the segment from both A and B. (4) Join the two points where the arcs cross. This line is the perpendicular bisector of AB.
How do you construct an angle bisector?▾
To bisect an angle: (1) Place the compass at the vertex and draw an arc cutting both arms of the angle. (2) From each intersection point, draw equal arcs inside the angle. (3) Draw a ray from the vertex through the point where these arcs meet. This ray bisects the angle.
What is tessellation and which regular polygons can tessellate?▾
Tessellation (or tiling) is covering a flat surface completely using one or more shapes without gaps or overlaps. Only three regular polygons can tessellate by themselves: equilateral triangles, squares, and regular hexagons, because their interior angles are divisors of 360°.
Why can a regular pentagon not tessellate a plane?▾
A regular pentagon has interior angles of 108°. When you try to fit pentagons around a single point, 3 pentagons give 3 × 108° = 324° (not 360°) and 4 pentagons give 4 × 108° = 432° (more than 360°). Since 108 does not divide 360 evenly, pentagons leave gaps or overlap and cannot tessellate.
What tools are used in geometric constructions and why?▾
The two tools used in classical geometric constructions are a compass (for drawing arcs and circles) and a straightedge or ruler (for drawing straight lines). Measurements are not used because constructions are based on geometric relationships rather than numerical lengths.
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