Playing with Constructions

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— all the angles are equal to 90° but opposite sides are not equal?

Give the lengths of the sides of a rectangle that cannot be divided into— two identical squares; three identical squares.

Construct a rectangle in which one of the diagonals divides the opposite angles into 60° and 30°.

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° and 40°.

Construct a rectangle in which one of the diagonals divides the opposite angles into 45° and 45°. 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.

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?