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08
NCERT Solutions · Maths Ch 8
Playing with Constructions
28 questions · 3 exercises
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Ex 8.1
Ex 8.2
Ex 8.3
NCERT answers with full exam-style working, step by step. Tap a question to open its solution.
1
EXERCISE 8.1 · 8 QUESTIONS
Artwork, Squares and Rectangles
Q1
Think: Imagine marking all the points that are 4 cm away from a point P. How would they look?
(1 mark)
Q2
Artwork (Wavy Wave): what radius should be taken in the compass to get the half circle in the figure? What should be the length of AX?
(2 marks)
Q3
Take a central line of a different length and try to draw the wave on it.
(2 marks)
Q4
Try to recreate the figure where the waves are smaller than a half circle (as in the neck of 'A Person'). The challenge is to get both waves identical.
(2 marks)
Q5
Which of the following is not a name for the square with corners S, P (top) and R, Q (bottom), i.e. S top-left, P top-right, R bottom-left, Q bottom-right? (1) PQSR (2) SPQR (3) RSPQ (4) QRSP
(3 marks)
Q6
Rectangle and four squares configuration (Fig. 8.3): draw it on dot paper so that the four squares are placed symmetrically around the rectangle.
(2 marks)
Q7
Identify if there are any squares in the collection A, B, C, D drawn on a dot grid. Can we reason without measuring?
(2 marks)
Q8
Draw at least 3 rotated squares and rectangles on a dot grid with corners on the dots. Verify if they satisfy their properties.
(2 marks)
2
EXERCISE 8.2 · 11 QUESTIONS
Constructing Squares and Rectangles
Q1
Construct a square PQRS of side 6 cm. State the steps.
(2 marks)
Q2
Draw a rectangle with sides of length 4 cm and 6 cm. After drawing, check whether it satisfies both rectangle properties.
(3 marks)
Q3
Draw a rectangle of sides 2 cm and 10 cm. After drawing, check if it satisfies both rectangle properties.
(3 marks)
Q4
Is it possible to construct a 4-sided figure in which all the angles are equal to 90° but the opposite sides are not equal?
(2 marks)
Q5
Rectangle ABCD with AB = 7 cm and BC = 4 cm. X moves on AD, Y moves on BC. Fill the table of XY: (X is 5 mm from A, Y is 3 cm from B); (1 cm, 1 cm); (2 cm, 4 cm).
(2 marks)
Q6
In the rectangle ABCD (AB = 7 cm), when X and Y are at the same distance from A and B (e.g. 5 mm and 5 mm; 1 cm and 1 cm; 1 cm 5 mm and 1 cm 5 mm), compare XY with AB and describe the shape ABYX. Where are X and Y closest and farthest?
(2 marks)
Q7
Construct a rectangle that can be divided into 3 identical squares. Also give side lengths of a rectangle that cannot be divided into (a) two identical squares, (b) three identical squares.
(3 marks)
Q8
A square within a rectangle: construct a rectangle of sides 8 cm and 4 cm. How will you construct a square inside, such that the centre of the square is the same as the centre of the rectangle?
(3 marks)
Q9
Falling squares and shadings: construct the figures (squares of side 4 cm, then squares of side 3 cm, 5 cm and 7 cm aligned as shown; a large square with shaded smaller squares).
(2 marks)
Q10
Square with a hole: a square has a circular hole whose centre is the centre of the square. Where should the centre of the circle be?
(2 marks)
Q11
Square with more holes and Square with curves (side 8 cm): where should the compass point be placed so that the arcs bulge uniformly?
(2 marks)
3
EXERCISE 8.3 · 9 QUESTIONS
Diagonals and Points Equidistant from Two Points
Q1
Diagonals of a rectangle: construct a rectangle PQRS, join the diagonals PR and QS and compare their lengths. Compare angles g and h, c and d. How should the rectangle be constructed so that a diagonal divides the opposite angles into equal parts?
(2 marks)
Q2
Construct a rectangle in which one of the diagonals divides the opposite angles into 60° and 30°.
(3 marks)
Q3
Construct a rectangle in which one of the diagonals divides the opposite angles into 50° and 40°.
(3 marks)
Q4
Construct a rectangle in which one of the diagonals divides the opposite angles into 45° and 45°. What do you observe about the sides?
(2 marks)
Q5
Construct a rectangle one of whose sides is 4 cm and the diagonal is 8 cm.
(3 marks)
Q6
Construct a rectangle one of whose sides is 3 cm and the diagonal is 7 cm.
(3 marks)
Q7
Construct the house: all the border lines are 5 cm (a square BCED with a triangle on top). Find the apex A. Then construct a bigger house in which all the sides are 7 cm.
(3 marks)
Q8
Try to recreate 'A Person', 'Wavy Wave' and 'Eyes' using the ideas of the House construction.
(2 marks)
Q9
Is there a 4-sided figure in which all the sides are equal in length but which is not a square? If it exists, can you construct it?
(3 marks)