CBSE Class 6 Mathematics Playing with Constructions Worksheet Set 01

Very Short Answer Questions

Question 1. A point O is marked on a page and many points are marked at a distance of 3 cm from O in every direction. Name the shape formed by all such points.
Answer:
They form a circle with centre O and radius 3 cm.

Teacher's Note:
1. All points at one fixed distance from a point make a circle.
2. The fixed point is the centre.

Question 2. Define the radius of a circle.
Answer:
The radius is the distance from the centre of a circle to any point on the circle. It is the same for every point of the circle.

Teacher's Note:
1. Mention both the centre and a point on the circle.
2. The same distance for all points is the key idea.

Question 3. Which instrument of the geometry box is used to draw circles and arcs?
Answer:
The compass. Its metal tip stays fixed at the centre and only the pencil tip is turned.

Teacher's Note:
1. The fixed tip marks the centre.
2. The opening of the compass is the radius.

Question 4. Which instrument do you use to measure an angle while checking a construction?
Answer:
The protractor, for example to check that a corner of a rectangle is 90°.

Teacher's Note:
1. A set square only checks right angles quickly.
2. A protractor can measure any angle.

Question 5. State the two properties that every rectangle has.
Answer:
R1: The opposite sides are equal in length.
R2: All four angles are 90°.

Teacher's Note:
1. Learn R1 and R2 by name.
2. Both must hold for a rectangle.

Question 6. State the two properties that every square has.
Answer:
S1: All four sides are equal in length.
S2: All four angles are 90°.

Teacher's Note:
1. S1 is about sides, S2 about angles.
2. Compare them with R1 and R2.

Question 7. A rectangle is named ABCD. Write any two other correct names for the same rectangle.
Answer:
BCDA and CDAB. (DABC, ADCB, DCBA, CBAD and BADC are also correct.)

Teacher's Note:
1. Start at any corner and go round in order.
2. Going the other way round is also allowed.

Question 8. How many diagonals does a rectangle have?
Answer:
A rectangle has two diagonals.

Teacher's Note:
1. One from each pair of opposite corners.
2. The two diagonals are equal in length.

Question 9. What is meant by a diagonal of a rectangle?
Answer:
A diagonal is the straight line joining two opposite corners of the rectangle.

Teacher's Note:
1. Opposite corners, not neighbouring corners.
2. A line joining neighbouring corners is a side.

Question 10. A square card is turned a little on the desk. Is it still a square? Give the reason in one line.
Answer:
Yes. Turning does not change its side lengths or its angles, so all sides stay equal and all angles stay 90°.

Teacher's Note:
1. Position does not change a shape's name.
2. Only sides and angles matter.

Question 11. What should be the gap between the compass tip and the pencil tip to draw a circle of radius 2.5 cm?
Answer:
The gap must be 2.5 cm, because the compass opening is the radius.

Teacher's Note:
1. Opening = radius.
2. Set it carefully against the ruler's scale.

Question 12. While drawing the “Eyes” artwork, some light lines are drawn that do not appear in the final figure. What is the use of such supporting lines?
Answer:
These supporting lines are not part of the final picture; they only help us fix the correct positions and keep the two curves of the eye alike.

Teacher's Note:
1. Draw supporting lines lightly so they can be rubbed out.
2. They are helpers, not part of the design.

Question 13. In a rectangle ABCD, AB = 9 cm. Write the length of CD and give the reason.
Answer:
CD = 9 cm, because AB and CD are opposite sides and opposite sides of a rectangle are equal (R1).

Teacher's Note:
1. AB and CD share no letter, so they are opposite.
2. Quote R1 as the reason.

Question 14. Write the first step you take while constructing a square of side 5 cm.
Answer:
Draw a line segment of 5 cm with a ruler; this is one side of the square.

Teacher's Note:
1. Every construction starts with one side.
2. Name the side, for example PQ = 5 cm.

Question 15. A perpendicular has been drawn at P on the line segment PQ, where PQ = 5 cm. How will you mark the point S on this perpendicular with PS = 5 cm without measuring again with a ruler?
Answer:
Open the compass to the length PQ (tips at P and Q). Keeping the metal tip at P, cut the perpendicular with the pencil: that point is S.

Teacher's Note:
1. A compass copies a length.
2. Do not change the opening after setting it.

Question 16. Why is a rough diagram drawn before starting a construction?
Answer:
A rough diagram helps us plan the construction: we see which lengths are equal and decide the order in which to draw the parts.

Teacher's Note:
1. Mark equal sides with small strokes in the rough diagram.
2. Planning avoids mistakes.

Question 17. Two identical half circles are drawn on a central line of length 10 cm so that they meet at its mid-point. What radius should be taken in the compass?
Answer:
Each half circle has diameter 10 ÷ 2 = 5 cm, so the radius is 5 ÷ 2 = 2.5 cm.

Teacher's Note:
1. Halve for the mid-point, halve again for the radius.
2. 5 cm is the diameter, not the radius.

Question 18. A rectangle is to be divided into two identical squares of side 3.5 cm each. What must the length of the rectangle be?
Answer:
The two squares sit side by side, so the length = 2 × 3.5 = 7 cm.

Teacher's Note:
1. The breadth is 3.5 cm.
2. Length = 2 × breadth for two squares.

Question 19. In a rectangle ABCD with AB = 8 cm, the point X on AD and the point Y on BC are each 2 cm from A and B respectively. Write the length XY and name the shape ABYX.
Answer:
XY = 8 cm (the same as AB), and ABYX is a rectangle.

Teacher's Note:
1. Equal distances from A and B give a straight-across line.
2. This is the shortest XY.

Question 20. A diagonal of a rectangle makes an angle of 25° with one side at a corner. What angle does it make with the other side at the same corner?
Answer:
The two parts add up to 90°, so the other angle is 90° − 25° = 65°.

Teacher's Note:
1. Corner angle = 90°.
2. Subtract the known part.

Question 21. How do the lengths of the two diagonals of a rectangle compare?
Answer:
The two diagonals of a rectangle are always equal in length.

Teacher's Note:
1. Check by measuring both in a drawing.
2. This holds for squares too.

Question 22. For which special rectangle does a diagonal divide the opposite angles into two equal parts?
Answer:
For a square, a rectangle with all four sides equal. Each part is then 45°.

Teacher's Note:
1. Equal parts happen only when all sides are equal.
2. 45° + 45° = 90°.

Question 23. Two points A and B are marked on a page. Write in one line how you will mark a point that is 6 cm from both A and B.
Answer:
Draw an arc of radius 6 cm with centre A and another of radius 6 cm with centre B; the point where the arcs cross is the required point.

Teacher's Note:
1. Keep the compass opening the same for both arcs.
2. Small arcs are enough.

Question 24. While constructing a rectangle whose one side is 4 cm and whose diagonal is 8 cm, which curve is drawn to fix the opposite corner, and with what radius?
Answer:
An arc (part of a circle) of radius 8 cm is drawn with its centre at the end of the side away from the perpendicular; where it cuts the perpendicular is the required corner.

Teacher's Note:
1. The radius equals the diagonal.
2. The arc is centred at the end where the diagonal starts.

Question 25. Is it possible to construct a four-sided figure in which all the angles are 90° but the opposite sides are not equal? Give the reason.
Answer:
No. If all four angles are 90° the figure is a rectangle, and by R1 its opposite sides must be equal.

Teacher's Note:
1. Four right angles always force R1.
2. Try drawing it; you will not succeed.

Question 26. Write the sides of one rectangle that cannot be divided into three identical squares, and give the reason.
Answer:
A rectangle of sides 7 cm and 2 cm: for three identical squares the length must be exactly 3 times the breadth, and 7 is not 3 × 2 = 6.

Teacher's Note:
1. Any example where length ≠ 3 × breadth is correct.
2. Always state the rule as the reason.

Question 27. A square of side 4 cm is drawn inside a rectangle of sides 8 cm and 4 cm so that both have the same centre. How far is each side of the square from the nearer shorter side of the rectangle?
Answer:
8 − 4 = 4 cm is left over and shared equally, so the gap is 4 ÷ 2 = 2 cm on each side.

Teacher's Note:
1. Same centre means equal gaps.
2. Subtract, then halve.

Question 28. In a rectangle ABCD, X moves along AD and Y moves along BC. When are X and Y farthest apart, and what does this greatest distance equal?
Answer:
When one is at A and the other at C (or one at D and the other at B). The greatest distance equals the length of a diagonal, AC or BD.

Teacher's Note:
1. Farthest apart means at opposite corners.
2. The two diagonals are equal, so either one can be named.

Question 29. Is there a four-sided figure in which all four sides are equal but which is not a square? Answer and explain in one line.
Answer:
Yes. A slanting figure with all four sides equal but angles not 90° (a rhombus) is not a square; it can be made with two arcs of equal radius.

Teacher's Note:
1. S1 holds but S2 fails.
2. Think of a pushed-over square.

Question 30. In the “Square with a Hole” construction, where must the centre of the circular hole be placed, and why?
Answer:
At the point where the two diagonals (lines joining opposite corners) cross, because that point is the centre of the square.

Teacher's Note:
1. The diagonals of a square cross at its centre.
2. Then the hole is the same distance from all four sides.