NCERT Solutions

Imagine marking all the points of 4 cm distance from the point P. How would they look?

For the 'Wavy Wave' figure, what radius should be taken in the compass to get this half circle? What should be the length of AX?

Take a central line of a different length and try to draw the wave on it.

Try to recreate the figure where the waves are smaller than a half circle (as appearing in the neck of the figure, 'A Person'). The challenge here is to get both the waves to be identical. This may be tricky!

Which of the following is not a name for this square?

Draw the rectangle and four squares configuration (shown in Fig. 8.3) on a dot paper. What did you do to recreate this figure so that the four squares are placed symmetrically around the rectangle? Discuss with your classmates.

Identify if there are any squares in this collection. Use measurements if needed.

Is it possible to reason out if the sides are equal or not, and if the angles are right or not without using any measuring instruments in the above figure? Can we do this by only looking at the position of corners in the dot grid?

Draw at least 3 rotated squares and rectangles on a dot grid. Draw them such that their corners are on the dots. Verify if the squares and rectangles that you have drawn satisfy their respective properties.

Draw a rectangle with sides of length 4 cm and 6 cm. After drawing, check if it satisfies both the rectangle properties.

Draw a rectangle of sides 2 cm and 10 cm. After drawing, check if it satisfies both the rectangle properties.

Is it possible to construct a 4-sided figure in which-

Is there a shorthand way of writing it down? In all the sentences, only the position of X, Y and the length XY changes. So we could write this as:

Have you checked what happens to the length XY when X and Y are placed at the same distance away from A and B, respectively? For example, as in the cases like these:

In each of these cases, observe

How does the farthest distance between X and Y compare with the length of AC? BD?

Construct a rectangle that can be divided into 3 identical squares.

Give the lengths of the sides of a rectangle that cannot be divided into—

A Square within a Rectangle: Construct a rectangle of sides 8 cm and 4 cm. How will you construct a square inside, as shown in the figure, such that the centre of the square is the same as the centre of the rectangle?

Falling Squares: Construct the figure.

Shadings: Construct this. Choose measurements of your choice. Note that the larger 4-sided figure is a square and so are the smaller ones.

Square with a Hole: Construct this.

Square with more Holes: Construct this.

Square with Curves: This is a square with 8 cm sidelengths.

How should the rectangle be constructed so that the diagonal divides the opposite angles into equal parts?

Construct a rectangle in which one of the diagonals divides the opposite angles into $60^\circ$ and $30^\circ$.

Construct a rectangle where one of its sides is 5 cm and the length of a diagonal is 7 cm.

Construct a rectangle in which one of the diagonals divides the opposite angles into $50^\circ$ and $40^\circ$.

Construct a rectangle in which one of the diagonals divides the opposite angles into $45^\circ$ and $45^\circ$. What do you observe about the sides?

Construct a rectangle one of whose sides is 4 cm and the diagonal is of length 8 cm.

Construct a rectangle one of whose sides is 3 cm and the diagonal is of length 7 cm.

House: Recreate this figure. Note that all the lines forming the border of the house are of length 5 cm.

Construct a bigger house in which all the sides are of length 7 cm.

Try to recreate 'A Person', 'Wavy Wave', and 'Eyes' from the section 'Artwork', using ideas involved in the 'House' construction.

Is there a 4-sided figure in which all the sides are equal in length but is not a square? If such a figure exists, can you construct it?