Class 7 Mathematics — Chapter 6: Constructions and Tilings

What you'll learn

• ▸Concept and Justification of the Perpendicular Bisector
• ▸Construction of a Perpendicular Bisector
• ▸Construction of a 90° Angle
• ▸Concept and Justification of Angle Bisection
• ▸Construction of an Angle Bisector
• ▸Application of Constructions in Designs
• ▸Historical Methods of Construction (Śulba-Sūtras)

Chapter Summary

--- PAGE 1 --- 6 CONSTRUCTIONS AND TILINGS 6.1 Geometric Constructions Eyes Do you recall the 'Eyes' construction we did in Grade 6? Of course, eyes can be drawn freehand, but we wanted to construct them so that the lower arc and upper arc of each eye look symmetrical. We relied on our spatial estimation to determine the two centres, A and B (see the figure), from which we drew the lower arc and upper arc respectively. The arcs define a line XY that 'supports' the drawing though it is not part of the final figure. We can start with this supporting line and systematically find the centres A and B. A • Y X • B For the eye to be symmetrical, or for the supporting line to be the line of symmetry, the upper and lower arcs should have the same radius. In other words, we must have AX = BX. Since AX = AY and BX = BY, this means AX = AY = BX = BY --- PAGE 2 --- Const…

Practice Questions from this Chapter

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1. Show real-world uses of geometric constructions. Get Solution →
2. Draw fascinating designs using only a compass. Get Solution →
3. Discover more about ancient Indian geometry. Get Solution →
4. What is the term for the division of a geometrical object into two identical parts? Get Solution →
5. What two simple tools are used for the geometric constructions described in this chapter? Get Solution →
6. What ancient Indian geometric texts dealt with the construction of fire altars? Get Solution →
7. According to the chapter, how can a 45° angle be constructed? Get Solution →
8. What is a line that bisects a given line segment and is also at a 90° angle to it called? Get Solution →

Did you know?

• 💡 Ancient Egyptians built huge pyramids using simple rope geometry.
• 💡 All of classical geometry was built using only a compass and straightedge.
• 💡 The Great Pyramid of Giza has sides that align almost perfectly with the cardinal directions.
• 💡 Hindu priests used detailed geometric instructions for their fire altars.
• 💡 The first known compasses were used by the ancient Greeks for drawing perfect circles.

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