Draw a rectangle with sides of length 4 cm and 6 cm. After drawing, check if it satisfies both the rectangle properties.
Answer
Steps of construction
Draw AB = 6 cm.
At A draw a perpendicular to AB; at B draw another perpendicular to AB.
Open the compass to 4 cm. With the tip at A cut the first perpendicular at D; with the tip at B cut the second perpendicular at C.
Join DC. ABCD is the required rectangle.
Rectangle ABCD with AB = 6 cm and AD = 4 cm. All four corners are right angles.
Checking the two properties
R1 AB = DC = 6 cm, AD = BC = 4 cm → opposite sides equal ✔
R2 ∠A = ∠B = ∠C = ∠D = 90° ✔
So the figure drawn is indeed a rectangle.
Q2.
Draw a rectangle of sides 2 cm and 10 cm. After drawing, check if it satisfies both the rectangle properties.
Answer
The steps are exactly the same, only the numbers change.
Draw PQ = 10 cm.
Draw perpendiculars to PQ at P and at Q.
Open the compass to 2 cm and cut both perpendiculars, at S (from P) and R (from Q).
Join SR. PQRS is the rectangle.
A long, thin rectangle: 10 cm by 2 cm. It is still a rectangle — the shape looks unusual but both properties hold.
R1 PQ = SR = 10 cm, PS = QR = 2 cm ✔
R2 ∠P = ∠Q = ∠R = ∠S = 90° ✔
Tip: for such a long rectangle, draw the 10 cm base along the long side of your notebook page and press the set square firmly, otherwise the two short sides come out slanting.
Q3.
Is it possible to construct a 4-sided figure in which — all the angles are equal to 90º but opposite sides are not equal?
Answer
No, it is not possible. If all four angles are right angles, the opposite sides are forced to be equal — you cannot escape it.
Try it and see what happens:
Draw AB, and draw perpendiculars to AB at A and at B. These two lines both make 90° with AB, so they run in the same direction — they are parallel and stay the same distance apart for ever.
Mark D on the first line and C on the second. For ∠D and ∠C to be 90° as well, DC must be perpendicular to both lines.
But the distance between two parallel lines is the same everywhere, so DC = AB, and D and C must be at the same height, so AD = BC.
All four angles 90° → opposite sides parallel → opposite sides equal
Why it happens: a four-sided figure has only four corners to play with. Once you fix all four angles at 90°, the only freedom left is the two lengths — and those lengths repeat on the opposite sides. So every 4-sided figure with four right angles is a rectangle (and if the two lengths are also equal, a square).
Try This: draw AB = 5 cm, perpendiculars at A and B, then mark AD = 3 cm and BC = 4 cm and join DC. Measure ∠D and ∠C — they will not be 90°, one is more and the other less.