Maths Class 6 Important Questions Chapter 8 Ganita Prakash

Playing with Constructions

Short Answer Questions

1. What is a circle?

Answer: A circle is a curve in which all points are at the same distance from a fixed point called the centre.

2. What is the radius of a circle?

Answer: The radius is the distance between the centre and any point on the circle.

3. What tool is used to draw a circle?

Answer: A compass is used to draw a circle.

4. What are the properties of a rectangle?

Answer:

• Opposite sides are equal.
• All angles are 90°.

5. What are the properties of a square?

Answer:

• All sides are equal.
• All angles are 90°.

6. What are diagonals of a rectangle?

Answer: The lines joining opposite corners of a rectangle are called diagonals.

7. Do diagonals of a rectangle have equal length?

Answer: Yes, both diagonals of a rectangle are equal.

8. Does rotating a square change its properties?

Answer: No, rotation does not change side lengths or angles, so it remains a square.

9. What is meant by opposite sides?

Answer: Opposite sides are the sides that lie across from each other in a figure.

10. What is a perpendicular line?

Answer: A line that makes a 90° angle with another line is called a perpendicular line.

Long Answer Questions

1. Explain why all points on a circle are at the same distance from its centre.

Answer: A circle is formed by marking all points that are at a fixed distance from a central point.

Step-by-step explanation:

1. Take a fixed point called the centre.
2. Fix a distance (called radius).
3. Mark many points that are exactly this distance from the centre.
4. Join these points smoothly to form a curve.

All these points are equally distant from the centre, so the figure formed is a circle.

Therefore, every point on a circle has the same distance from its centre.

2. A rectangle has length 8 cm and breadth 5 cm. Check whether it satisfies rectangle properties.

Answer:

Given:
Length = 8 cm, Breadth = 5 cm

Step-by-step verification:

1. Opposite sides:
   • Length sides = 8 cm and 8 cm → equal
   • Breadth sides = 5 cm and 5 cm → equal
2. Angles:
   • All angles in a rectangle are 90°

Conclusion: The figure satisfies both conditions:

• Opposite sides are equal
• All angles are 90°

So, it is a rectangle.

3. Explain how rotation does not change a square.

Answer: Step-by-step explanation:

1. A square has all sides equal and all angles 90°.
2. When the square is rotated, its position changes but not its size or shape.
3. The lengths of all sides remain the same.
4. The angles remain 90°.

Conclusion:
Since both properties remain unchanged, the rotated figure is still a square.

4. Compare a square and a rectangle based on their properties.

Answer: Step-by-step comparison:

Conclusion:

• Every square is a rectangle (because it satisfies rectangle properties).
• But every rectangle is not a square (because all sides are not equal).

5. Explain how you can identify the nearest and farthest positions between two moving points on opposite sides of a rectangle.

Answer: Step-by-step explanation:

1. Consider two points moving along opposite sides of a rectangle.
2. Measure the distance between the two points in different positions.

Nearest position:

• When both points are directly opposite each other (perpendicular distance).
• This gives the shortest distance.

Farthest position:

• When the points are at opposite corners of the rectangle.
• This distance is along the diagonal and is the longest.

Conclusion:

• Minimum distance is along a straight perpendicular line.
• Maximum distance is along the diagonal of the rectangle.