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Playing with Constructions

NCERT Class 6 · Mathematics Based on NCERT Class 6 Mathematics textbook · Free CBSE study kit

Chapter Notes

**Circle:** A shape made of all points exactly the same distance (radius) from a centre point P. Use compass to draw: fix point at P, open compass to radius r, rotate pencil around P.

**Radius:** Distance from circle's centre to any point on the circle. All radii of same circle are equal.

**Square Properties:** (1) All four sides equal length. (2) All four angles = 90°. Works when rotated.

**Rectangle Properties:** (1) Opposite sides equal length. (2) All four angles = 90°. Works when rotated.

**Naming Shapes:** Must list corners in order as you travel around shape. ABCD, BCDA, CDAB, DABC are valid. ABDC is not valid.

**Drawing Square of side 6 cm:** Draw line PQ = 6 cm → draw perpendicular at P, mark S at 6 cm → draw perpendicular at Q, mark R → join SR.

**Drawing Rectangle 4 cm × 6 cm:** Same steps as square but mark perpendiculars at 4 cm and 6 cm lengths instead of equal sides.

**Diagrams to Remember:** (1) Compass with radius marked from centre. (2) Rectangle ABCD with opposite sides labelled equal. (3) Square corners showing 90° angles.

**Don't Confuse:** Square IS a special rectangle (all sides equal). Rotating doesn't change a square into rectangle — it stays square. Radius ≠ Diameter (radius is half).

MCQs — 10 Questions with Answers

Q1. What is the distance from the centre of a circle to any point on the circle called?

  • A. Radius ✓
  • B. Diameter
  • C. Circumference
  • D. Chord

Answer: A — Radius is defined as the distance between the centre and any point on the circle.

Q2. Which property is true for both squares and rectangles?

  • A. All sides are equal
  • B. All angles are 90° ✓
  • C. Opposite sides are equal and parallel
  • D. Only one pair of sides is equal

Answer: B — Both squares and rectangles have all four angles equal to 90°; however, only squares have all sides equal.

Q3. If you rotate a square 45°, what happens to it?

  • A. It becomes a rectangle
  • B. It becomes a diamond shape but stays a square ✓
  • C. It is no longer a square
  • D. Its sides become unequal

Answer: B — Rotation does not change the lengths of sides or angles, so a rotated square is still a square, even if it looks diamond-shaped.

Q4. To draw a circle using a compass, what must you keep fixed?

  • A. The pencil tip
  • B. The sharp point (centre) ✓
  • C. Both the sharp point and pencil equally
  • D. Only the ruler

Answer: B — You must keep the sharp point fixed at the centre P while rotating the pencil to draw the circle.

Q5. In rectangle ABCD, which sides are called opposite sides?

  • A. AB and BC
  • B. AB and CD, and also AD and BC ✓
  • C. All four sides are opposite
  • D. Only AB and AD are opposite

Answer: B — Opposite sides are sides that do not share a corner; AB is opposite to CD, and AD is opposite to BC.

Q6. Which of the following is NOT a valid name for square PQRS?

  • A. QRSP
  • B. RSPQ
  • C. PQSR ✓
  • D. SPQR

Answer: C — PQSR jumps from P to Q to S, skipping R in order; valid names must follow the corners in travelling order like PQRS, QRSP, RSPQ, or SPQR.

Q7. What are all the angles of a square equal to?

  • A. 60°
  • B. 45°
  • C. 90° ✓
  • D. 180°

Answer: C — A square has all four angles equal to 90° (right angles), which is one of its defining properties.

Q8. You need to construct a rectangle with sides 3 cm and 5 cm. After drawing it, what should you verify?

  • A. Only that all sides are equal
  • B. Only that all angles are 90°
  • C. That opposite sides are equal and all angles are 90° ✓
  • D. That all four sides are exactly equal

Answer: C — To verify a rectangle, you must check both rectangle properties: opposite sides equal (3 cm opposite 3 cm, 5 cm opposite 5 cm) and all angles 90°.

Q9. In the diagram, point P is the centre and the distance PQ is 4 cm. If R is another point on the circle, what is the distance PR?

  • A. 2 cm
  • B. 4 cm ✓
  • C. 8 cm
  • D. Cannot be determined

Answer: B — All points on a circle are at the same distance (radius) from the centre; since PQ = 4 cm and Q is on the circle, PR must also equal 4 cm.

Q10. A square has one side measuring 7 cm. What is the length of the opposite side?

  • A. 3.5 cm
  • B. 7 cm ✓
  • C. 14 cm
  • D. Cannot be determined

Answer: B — In a square, all four sides are equal; if one side is 7 cm, the opposite side (and all other sides) must also be 7 cm.

Flashcards

What is the centre of a circle?

The fixed point P from which all points on the circle are equally distant.

What is the radius of a circle?

The distance between the centre and any point on the circle.

Name two properties of a rectangle.

Opposite sides are equal in length, and all angles are 90 degrees.

Name two properties of a square.

All four sides are equal in length, and all angles are 90 degrees.

How do you use a compass to draw a circle?

Open the compass to the radius length, fix the sharp point at the centre, and rotate the pencil around while keeping the point fixed.

Is a rotated square still a square?

Yes, because rotation does not change the lengths of sides or the angles, so it still satisfies both square properties.

How should you name a rectangle ABCD in other valid ways?

You can use BCDA, CDAB, or DABC — corners must be listed in order as you travel around the rectangle.

What angle do all corners of a rectangle have?

All corners of a rectangle have a right angle of 90 degrees.

What is the difference between a square and a rectangle?

A square has all four sides equal, while a rectangle has only opposite sides equal; both have all angles of 90 degrees.

What tools do you need to construct a perfect square or rectangle?

A ruler to draw straight lines, a compass to create right angles and circles, and a set square to check angles.

Important Board Questions

What is a radius of a circle? [1 mark]

It is the distance from the centre to any point on the circle. All radii of the same circle are equal.

List any two properties of a square. [2 marks]

Think about the sides and the angles. A square must have all sides equal and all angles equal to 90°.

How would you use a compass to draw a circle with radius 5 cm? Explain the steps clearly with an example from your daily life where you might need to draw such a circle. [3 marks]

First, open the compass to 5 cm using a ruler. Then fix the sharp point at centre P and rotate the pencil around it. Example: drawing a circular plate design or a pizza cutter template.

Draw a rectangle ABCD with sides 4 cm and 6 cm. After drawing, verify that it satisfies both the properties of a rectangle by taking measurements. Write down what you measured and what you found. [5 marks]

Use ruler to draw sides: AB = 4 cm, BC = 6 cm, CD = 4 cm, DA = 6 cm. Check: (1) Are opposite sides equal? (2) Are all angles 90° using a set square? State your findings clearly.

True or False: A rotated square is no longer a square because it looks like a diamond. Give a reason for your answer. [2 marks]

Check if rotation changes the side lengths or angles. A square remains a square after rotation because its properties (equal sides and 90° angles) do not change.

Next chapterSymmetry →

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