Construct a Square within a Rectangle

Transcript

Construct a Square within a RectangleConstruct 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? Now, the square inside would have maximum side as 4 cm So, square would be 4 × 4 Our figure looks like Also, labelling the sides Now, ABCD is a rectangle & EFGH is a square Also, all angles are 90° ∴ ∠ A = ∠ B = ∠ C = ∠ D = 90° We draw the rectangle using 2 sides, and 3 angles Steps of construction 1. Draw side AB of length 8 cm 2. Now, we draw 90° from point A 3. Now, we draw 90° from point B Taking 4 cm as radius, and B as center, draw an arc. Where the arc intersects the line is point C Now, make 90° from point C Mark point D where the lines from point A and point C intersect 7. Now keeping compass as same 2 cm open, draw an arc from point A on AB – marking point AB 8. Similarly, keep pointy end on B, compass same 2 cm open and mark point F To mark H and G – we can use two methods Method 1 – Make 90° from point E and point F and intersect line CD at point H and G respectively Method 2 – Mark 2 cm from point D to mark point H and 2 cm from point C to mark point G 9. Using Method 2 to make points H and G 10. Join EH and FG Thus, this is our required figure