Drawing rectangles and squares

Draw Rectangle A B C D where A B equals 6 centimetres and the breadth B C is half the length, on the grid below. Each small square of the grid is 1 centimetre by 1 centimetre. Letter the vertices in order, label both lengths and mark the right angles. Try it first. Pause if you like. We may choose where to start on the empty grid. For a side of 6 centimetres, do we count six dots or six intervals? Draw straight line A B, 6 centimetres long. Count six intervals along a row. Label the ends A and B. Six intervals pass seven dots, including the starting dot. The spaces between neighbouring dots give the length. The breadth B C is 6 divided by 2, which equals 3 centimetres. From B, draw three intervals upwards, perpendicular to A B. Label C. Draw straight line A D, parallel to B C, 3 centimetres long. Start from A and go up the same three intervals. Label D. Draw line D C to complete the rectangle. Join the two top vertices along their row. Mark all four right angles. Check that A B is labelled 6 centimetres and B C is labelled 3 centimetres. The letters go around the boundary in order. Opposite sides are equal and parallel, and every corner is a right angle.

Draw Square A B C D of side 3 centimetres on the grid below. Each small square of the grid is 1 centimetre by 1 centimetre. Letter the vertices in order, mark the right angles and mark the equal sides. Try it first. Pause if you like. A square needs four equal sides as well as four right angles. How many intervals should each side cross? Draw straight line A B, 3 centimetres long. Count three intervals, from the starting dot to the fourth dot. Label A and B. Draw perpendicular line B C, 3 centimetres long. Go up three intervals from B. Label C. Draw straight line A D, parallel to B C, 3 centimetres long. Label D. Draw line D C to complete the square. The top side is also three intervals long. Mark the right angles at all four corners, and put the same equal-side mark on all four sides. Count the intervals, turn at right angles, and finish the labels and marks.