Class 6 Mathematics Chapter 8 Playing With Constructions

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I. Chapter Summary:

This chapter introduces students to the basic concepts and techniques of geometrical constructions using a ruler and a compass. Students learn to construct basic geometric figures such as line segments, perpendicular lines, and angles. The chapter emphasizes practical skills in accurately drawing and measuring geometric shapes, understanding the properties of perpendicular and parallel lines, and constructing bisectors of line segments and angles. These foundational skills prepare students for advanced geometric problem-solving.

II. Key Concepts Covered:

• Basic Tools: Understanding the use of ruler and compass in constructions.

• Line Segment Construction: Drawing a line segment of given length using a ruler.

• Perpendicular Lines: Constructing perpendiculars to a line segment at a point on the line and at a point outside the line.

• Angle Construction: Constructing angles using compass arcs.

• Bisectors: Constructing perpendicular bisectors of line segments and angle bisectors.

• Properties of Constructed Figures: Understanding the significance of perpendicularity and bisectors in geometry.

III. Important Questions:

(A) Multiple Choice Questions (1 Mark):

1. Which tool is used to draw arcs in geometric constructions?
   a) Ruler
   b) Protractor
   c) Compass
   d) Set square
   Answer: c) Compass
   (PYQ 2022)

2. A perpendicular drawn to a line segment at one of its endpoints forms an angle of:
   a) 45°
   b) 60°
   c) 90°
   d) 180°
   Answer: c) 90°
   (PYQ 2021)

3. The perpendicular bisector of a line segment divides it into:
   a) Two unequal parts
   b) Two equal parts
   c) Three parts
   d) None of these
   Answer: b) Two equal parts

4. The point where two bisectors meet is called:
   a) Incenter
   b) Circumcenter
   c) Centroid
   d) Orthocenter
   Answer: a) Incenter

(B) Short Answer Questions (2/3 Marks):

1. Describe how to construct a perpendicular to a line segment at a point on it.

2. What is a compass used for in constructions?

3. Explain the steps to construct an angle bisector.

4. How do you construct a perpendicular to a line from a point outside it?

(C) Long Answer Questions (5 Marks):

1. Construct a perpendicular bisector of a given line segment and explain the steps.

2. Describe the process to construct a 60° angle using a compass and ruler.

3. Explain the significance of angle bisectors in triangle constructions.

4. Construct perpendiculars from a point outside a given line segment and describe the method.

(D) HOTS (Higher Order Thinking Skills) Questions:

1. Why is a compass necessary for constructing perpendicular bisectors instead of only a ruler? Explain.

2. If two perpendicular bisectors of a triangle intersect at a point, what does this point represent? Explain its importance.

IV. Key Formulas/Concepts:

• No numerical formulas; focus on construction techniques and properties.

• Definitions: perpendicular lines, bisectors, arcs, compass usage.

• Properties: perpendicular bisector divides line segment equally; angle bisector divides angle into two equal parts.

V. Deleted Portions (CBSE 2025–2026):

No portions have been deleted from this chapter as per the rationalized NCERT textbooks.

VI. Chapter-Wise Marks Bifurcation (Estimated – CBSE 2025–2026):

VII. Previous Year Questions (PYQs):

• 2022: MCQ on compass usage (1 mark)

• 2021: Short answer on perpendicular construction (2 marks)

• 2020: Long answer on angle bisector construction (5 marks)

• 2019: HOTS question on properties of bisectors (3 marks)

VIII. Real-World Application Examples to Connect with Topics:

• Architectural design requiring precise geometric constructions.

• Engineering drawings using compasses and rulers.

• Creating accurate models in carpentry and metalwork.

• Navigational tools involving geometric principles.

IX. Student Tips & Strategies for Success:

• Practice using compass and ruler for accuracy and confidence.

• Follow step-by-step instructions carefully during constructions.

• Draw lightly first, then darken lines once verified.

• Attempt previous years’ construction problems for practice.

X. Career Guidance & Exploration:

• For Classes 9–10:

  • Geometry skills useful in Science, Commerce, Arts streams.

  • Helpful for exams requiring spatial reasoning like NTSE, Olympiads.

• For Classes 11–12:

  • Essential for careers in Engineering, Architecture, Design, and Surveying.

  • Preparation for competitive exams such as JEE and NATA includes construction questions.

XI. Important Notes:

• Always check the official CBSE syllabus for updates.

• Accuracy in construction is key — practice regularly.

• Understand the geometric principles behind each construction step.