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