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Practice Time 8C

4 cm
1. Construct a rectangle of sides 4 cm and 2 cm. How will you construct a
square inside, as shown in the figure, such that the centre of the square 2 cm
is the same as the centre of the rectangle?
2. Check the falling squares given alongside:
Construct the same falling squares with sides 6 cm each. Make sure that the squares
are aligned in the same way they are shown.
3. Construct a rectangle with one of its sides 4 cm and divide it into three identical squares.
4. Give the lengths of the sides of a rectangle that cannot be divided into:
(a) Two identical squares (b) Three identical squares.
5. Construct the rectangle and square with holes as shown below.

(a) (b)

6. Construct a square of 12 cm and make 8 squares each of side 3 cm inside it. Then
divide these square diagonally and shade the triangles as shown alongside.

Exploring Diagonals of Rectangles and Squares

Consider a rectangle ABCD and join AC and BD. These A B
two lines are called the diagonals of the rectangle ABCD. s t
r u
In rectangle ABCD, the right angles at A and C are called
opposite angles. B and D are also called the other pair
of opposite angles.
A diagonal splits each pair of opposite angles into two
smaller angles. For example, in the adjoining figure, the q p w v
diagonal AC divides angle C into two smaller angles, i.e., D C
v and w. Similarly, the diagonal AC also divides the angle A into two smaller angles, i.e., r and s.

Maths Talk
• Measure AC and BD and discuss with your classmates.
• Does the diagonal bisect the opposite angles? Observe the figure and think about the answer. Verify your
answer by measuring them actually.
• Are s and w equal? Are v and r equal? First predict the answer then measure them. Identify other pairs of equal
angles and discuss.
• Construct a square and draw its diagonals. Check whether the diagonals are equal in length. Does the diagonal
bisect the opposite angles? Discuss about the answers with your classmates.

243 Playing with Constructions