Class 7 Mathematics — Chapter 6: Constructions and Tilings
Chapter 6: Constructions and Tilings is a chapter in Class 7 Mathematics (Ganita Prakash Part 2), part of the CBSE NCERT curriculum followed by over 25 million students across India. This chapter covers 7 topics including Concept and Justification of the Perpendicular Bisector, Construction of a Perpendicular Bisector, Construction of a 90° Angle. BrainWeave provides free AI-powered explanations — by voice or text, in Hindi or English — with no signup required.
What you'll learn
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▸Concept and Justification of the Perpendicular BisectorCore conceptperpendicular bisectorbisectioncongruenceequidistantmidpoint
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▸Construction of a Perpendicular BisectorCore conceptconstructioncompassrulerintersecting arcsline segment
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▸Construction of a 90° AngleCore concept90 degree angleright angleperpendicularpoint on a lineconstruction
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▸Concept and Justification of Angle BisectionCore conceptangle bisectorbisectequal anglesSSS congruencevertex
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▸Construction of an Angle BisectorCore conceptconstructionangle bisectorcompassvertexarcs
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▸Application of Constructions in Designsgeometric designpatterns45 degree angleapplicationsupporting lines
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▸Historical Methods of Construction (Śulba-Sūtras)Śulba-SūtrasVedic mathematicsropehistorical contextancient India
Chapter Summary
Understanding that a perpendicular bisector is a line that divides another line segment into two equal parts at a 90-degree angle. Students should grasp the proof based on triangle congruence (SSS and SAS) which demonstrates that any point equidistant from the endpoints of a segment must lie on its perpendicular bisector.
Mastering the step-by-step method to construct the perpendicular bisector of a given line segment using only a compass and an unmarked ruler. This involves drawing intersecting arcs from the endpoints of the segment and joining the intersection points.
Learning to apply the perpendicular bisector construction method to create a 90-degree angle at a specific point on a given line. This involves marking two points equidistant from the given point to form a segment, and then constructing its perpendicular bisector through that point.
Understanding that an angle bisector is a ray that divides an angle into two equal, adjacent angles. Students should understand the justification for the construction method, which relies on creating two congruent triangles using the SSS congruence condition.
Mastering the practical steps to bisect any given angle using a compass and ruler. This involves drawing an arc from the vertex to intersect the arms of the angle, and then drawing two intersecting arcs from those intersection points.
Recognizing how fundamental constructions like angle bisection (e.g., creating a 45° angle by bisecting a 90° angle) and perpendicular bisectors are used as supporting lines to create more complex geometric designs and patterns.
Gaining an appreciation for the historical context of geometric constructions, particularly the methods described in the ancient Indian Śulba-Sūtras, which used tools like ropes to perform constructions such as finding a perpendicular bisector.
Practice Questions from this Chapter
Tap "Get Solution" on any question to ask our AI tutor.
- Show real-world uses of geometric constructions. Get Solution →
- Draw fascinating designs using only a compass. Get Solution →
- Discover more about ancient Indian geometry. Get Solution →
- What is the term for the division of a geometrical object into two identical parts? Get Solution →
- What two simple tools are used for the geometric constructions described in this chapter? Get Solution →
- What ancient Indian geometric texts dealt with the construction of fire altars? Get Solution →
- According to the chapter, how can a 45° angle be constructed? Get Solution →
- 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.
Frequently Asked Questions
How many topics are covered in this chapter?
This chapter covers 7 key topics: 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, and more. The BrainWeave AI tutor explains each one with examples.
Is Chapter 6: Constructions and Tilings important for board exams?
Class 7 is a foundation year. Mastering this chapter now will help you build strong fundamentals for the higher classes.
Can I get NCERT solutions for this chapter in Hindi?
Yes. BrainWeave's AI tutor supports Hindi, English, and Hinglish for both voice and text chat. Just ask your question in your preferred language.
Is BrainWeave free for Class 7?
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Can I use voice chat for this chapter?
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