TalentJR

Playing with Constructions – Class 6 Maths Chapter 8 Notes & NCERT PDF

Class 6MathematicsChapter 8NCERT book: Ganita Prakash - Mathematics Class 6

Notes and a simple summary of Chapter 8 of the NCERT Class 6 Mathematics book, with the official chapter PDF, flashcards, an MCQ quiz and an AI tutor for your doubts.

🎧 Listen to the content

Chapter 8: Playing with Constructions

Introduction

Chapter 8 turns the geometry notebook into an art studio. It starts with some pictures (a person, a wavy wave, a pair of eyes). Children first try them freehand, then pick up a ruler and a compass and learn to draw them exactly. On the way they rediscover the circle, write down what makes a rectangle and a square, and learn a planning habit mathematicians use: draw a rough diagram first, then construct.

Key Ideas

8.1 Artwork: the compass and the circle

  • Mark a point P and many points 4 cm away from it in all directions. Joined up, they make a circle.
  • To draw it, open the compass against a ruler so the gap between the metal tip and the pencil is 4 cm. Keep the tip fixed on P and turn only the pencil.
    • All the points of a circle are at the same distance from its centre. This distance is called the radius.
  • Wavy Wave: take a central line AB = 8 cm. The first wave is a half circle over half the line, so AX = 4 cm and the compass radius is 2 cm.
  • A Person and Eyes: the hard part is choosing where to place the compass tip and what radius to use for a curve. Estimate, try and adjust.

    • 8.2 Squares and rectangles

    In rectangle ABCD, A, B, C, D are the corners, AB, BC, CD, DA are the sides, and AB and CD are opposite sides.

    Rectangle: R1) opposite sides are equal; R2) all angles are 90°.
    Square: S1) all sides are equal; S2) all angles are 90°.
  • Naming: a valid name lists the corners in order of travel around the figure, starting from any corner. ABCD, BCDA, ADCB and DCBA are fine; ABDC and ACBD are not. For the square in the book, PQSR is not a valid name.
  • Rotated squares and rectangles: turning a square does not change its lengths or angles, so a tilted square is still a square. The same goes for a rectangle. On a dot grid you can even check this without measuring, just from where the corners sit on the dots.

    • 8.3 Constructing a square (side 6 cm)

  • Draw PQ = 6 cm.
  • Draw a perpendicular to PQ through P.
  • Mark S on it so that PS = 6 cm, with a ruler (Method 1) or a compass (Method 2).
  • Draw a perpendicular to PQ through Q.
  • Mark R on it so that QR = 6 cm. A compass already set to 6 cm makes this quick.
  • Join SR. Check that RS = 6 cm and that ∠R = ∠S = 90°.

    • 8.4 An exploration in rectangles

    Rectangle ABCD has AB = 7 cm and BC = 4 cm. Point X slides along AD and point Y slides along BC.

  • When X and Y are the same distance from A and B, XY = AB = 7 cm and ABYX is a rectangle. This is also the shortest XY can be.
  • XY is longest when it is a diagonal (AC or BD).
  • Record trials in a table: Distance of X from A | Distance of Y from B | Length of XY.

    • Breaking rectangles: for a rectangle made of 2 identical squares, the long side is twice the short side. For 3 squares, it is three times. Draw a rough figure and mark equal sides with a small tick (|). You can transfer a length with a compass without measuring it.

    8.5 Diagonals of rectangles and squares

  • The two diagonals of a rectangle are equal.
  • A diagonal splits each opposite angle into two parts. These parts are equal (45° and 45°) only when the rectangle is a square.
  • Construction with angles: to make a rectangle whose diagonal splits the corner angles into 60° and 30°: (1) draw AB of any length; (2) draw a perpendicular at B and a line from A making 60° with AB — they meet at C, so diagonal AC splits ∠A into 60° and 30°; (3) draw a perpendicular to AB through A, since D lies on it; (4) find D either with a perpendicular to BC at C ("all angles are 90°") or by marking AD = BC with a compass ("opposite sides are equal").
  • Given a side and a diagonal (5 cm and 7 cm): draw DC = 5 cm and a perpendicular line l at C. B lies on l and 7 cm from D. So draw an arc of radius 7 cm centred at D. Where it cuts l is B. Then draw perpendiculars at D and B to get A.

    • 8.6 Points equidistant from two given points

    The House: every border line is 5 cm. The roof tip A must be 5 cm from both B and C. Draw an arc of radius 5 cm from B and another from C. Where they cross is A, with no trial and error. The curved roof is then an arc of radius 5 cm centred at A.

    Worked Examples

    1. Wavy Wave. AB = 8 cm, split into two half-circle waves. Each wave sits on 4 cm, so AX = 4 cm and the compass radius = 4 ÷ 2 = 2 cm.

    2. Two-square rectangle. If AF = 4 cm, then AB = AF = 4 cm and BC = 4 cm, so AC = 8 cm.

    3. Rectangle with a 5 cm side and a 7 cm diagonal

  • Draw DC = 5 cm.
  • Draw line l perpendicular to DC at C.
  • With centre D and radius 7 cm, draw an arc cutting l at B.
  • Draw perpendiculars to DC at D and to BC at B. They meet at A.
  • Check R1 and R2.

    • 4. Diagonal splitting 50° and 40°. 50° + 40° = 90°, so the pieces fit in a right angle. Build the 50° angle at one corner, then complete the rectangle as in the 60°/30° example.

    5. Diagonal splitting 45° and 45°. The sides come out equal, so the rectangle is a square.

    Figure it Out: Hints

  • Can a 4-sided figure have all angles 90° but opposite sides unequal? No. Try it and the sides refuse to close.
  • A rectangle that cannot be split into two identical squares: for example, 4 cm × 2.5 cm (the long side isn't twice the short side).
  • Square with a hole: the circle's centre is where the two diagonals of the square meet.
  • A 4-sided figure with all sides equal that is not a square: it exists. Use the House idea: find the fourth point D, 5 cm from both B and C, with two arcs.

    • Maths Words

  • Compass (परकार), Ruler (पैमाना)
  • Circle (वृत्त), Centre (केंद्र), Radius (त्रिज्या)
  • Arc (चाप), Curve (वक्र)
  • Rectangle (आयत), Square (वर्ग)
  • Corner (कोना/शीर्ष), Opposite sides (सम्मुख भुजाएँ)
  • Perpendicular (लम्ब), Right angle (समकोण)
  • Diagonal (विकर्ण)
  • Rough diagram (कच्चा चित्र)
  • Equidistant (समदूरस्थ)

    • Common Mistakes

  • Letting the compass tip slip, or its opening change, while drawing a circle.
  • Naming a rectangle "ABDC": the letters must follow the boundary.
  • Thinking a tilted square is a "diamond" and not a square. Check S1 and S2!
  • Using trial and error with a ruler when one arc would locate the point exactly.
  • Assuming every rectangle's diagonal splits the corner angles equally. That only happens in a square.
  • Skipping the rough diagram, then not knowing which line to draw first.

    • Maths in Daily Life

    Carpenters, tailors, architects and rangoli artists all use these ideas. A mason marks a right angle, a gardener draws a circular flower bed with a rope and a peg, and an architect plans a house front before building it.

    💡 Key Learning Points

    • ✓A circle is the set of all points at the same distance (radius) from its centre; a compass draws it exactly.
    • ✓A rectangle has opposite sides equal and all angles 90°; a square has all sides equal and all angles 90° — rotating them does not change this.
    • ✓Squares and rectangles can be constructed step by step using perpendiculars and a compass to transfer lengths.
    • ✓A rectangle can be constructed from its two sides, or from one side and a diagonal, by using an arc to locate the missing corner.
    • ✓A point at given distances from two points is found where two arcs intersect — making a rough diagram first helps plan the construction.

    👨‍🏫 Teaching Tips

    • →Begin with the Artwork page: let children draw freehand first, then with compass — discuss which looked better and why.
    • →Practise safe compass handling: set the radius against a ruler, keep the tip fixed, rotate only the pencil.
    • →Use dot paper for rotated squares so children reason about equal sides and right angles from dot positions.
    • →Run the X–Y sliding exploration in pairs with a recording table; ask them to predict before measuring.
    • →Insist on a labelled rough diagram with equal-side ticks before every construction; ask 'Which line can be drawn first?'.
    • →Demonstrate the 5 cm side + 7 cm diagonal rectangle live, contrasting ruler trial-and-error with the single arc.
    • →End with the House: let each child build a 7 cm house and exhibit the constructions on the class wall.

    📋 Assessment Questions

    1. Can the student draw a circle of a given radius and explain what 'radius' means?
    2. Can the student state properties R1, R2 and S1, S2 and identify valid names like ABCD vs ABDC?
    3. Can the student construct a square of side 6 cm and a rectangle given a side and a diagonal, listing the steps?
    4. Can the student locate a point equidistant from two given points using two arcs?
    5. Can the student explain when a diagonal splits the corner angles equally (only in a square)?

    Ask the AI tutor about Class 6 Mathematics Chapter 8

    Get question answers, important questions, a quick MCQ quiz or a simple explanation of “Playing with Constructions”. Free — sign in with Google.

    How the AI tutor works →

    👩‍🏫 Class 6 Mathematics classes near you — online or at home

    Prefer a real teacher? TalentJR teachers take live online classes anywhere in India and visit homes in selected cities. Tell us what you need and our team will call you with timings and fees.

    • Live online classesSmall groups or 1:1 with a teacher, from home, any city.
    • Teacher at homeA TalentJR teacher visits your home (selected cities).
    • At a centreClasses at a TalentJR partner centre near you, where available.

    Keep learning

    All chapters in Ganita Prakash - Mathematics Class 6

    1. 1. Patterns in Mathematics
    2. 2. Lines and Angles
    3. 3. Number Play
    4. 4. Data Handling and Presentation
    5. 5. Prime Time
    6. 6. Perimeter and Area
    7. 7. Fractions
    8. 8. Playing with Constructions
    9. 9. Symmetry
    10. 10. The Other Side of Zero