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Step 4: Similarly, draw a perpendicular to PQ
through Q and mark point R on the perpendicular
such that QR = 4 cm.

Join RS.
Step 5: Thus, PQ = SR = 6 cm, PS = QR = 4 cm, and
∠P = ∠Q = ∠R = ∠S = 90°.

Therefore, PQRS is a rectangle, as it satisfies all the
properties of a rectangle.
Practice Time 8B

1. Draw a rectangle of sides 3 cm and 9 cm. After drawing, check if it satisfies both the rectangle
properties.

2. Draw a square of side 6 cm. Check if it satisfies the square properties.
3. Draw a rectangle when its sides are 5 cm and 6.2 cm.

4. Draw a square when one side is 4.5 cm.
More about Rectangles

Consider a rectangle PQRS with PQ = 9 cm and QR = 5 cm.
Imagine two movable points X and Y. X, which can be placed anywhere along the side PS, and Y,
which can be placed anywhere along the side QR.

P Q P Q = Y P Q

2 cm
Y
X
1 cm
S R S = X R S = X R = Y
Now a lot of questions arise.

• Where will points X and Y be closest to each other?
• Where will points X and Y be the farthest apart?

To find out how close or far apart two points, X and Y, are on a rectangle, we should follow these
steps:

1. Place points X and Y somewhere on the sides of the rectangle.
2. Measure the distance between X and Y using a ruler.

3. Compare this distance to the length of one side of the rectangle (called PQ).
4. Try moving points X and Y to different places on the rectangle and measuring again. See if
there are other positions where X and Y are the closest or farthest from each other.

You will find that points X and Y are closest when X is at P and Y is at R, or when XY is parallel to QR.
On the other hand, X and Y are farthest apart when X is at S and Y is at Q, or when X is at P and Y is at R.

239 Playing with Constructions