Page 227 - Ganit Kaushal

8.6 CONSTRUCTING SQUARES AND RECTANGLES

1. When Sides are Given

Construction 5: Construct a square PQRS with a side of 6 cm.

Sol. Follow the steps given below:
P 6 cm Q
Step 1: Draw a line PQ = 6 cm, with the help of a ruler as shown in the figure (i). (i)
Step 2: Draw a perpendicular to the
line PQ at the point P with the help of
a protractor as shown in Figure (ii).
Similarly, draw the perpendicular to
the line PQ at the point Q with the
help of a protractor as shown in the P 6 cm Q P 6 cm Q
adjoining figure (iii). (ii) (iii)

After completing step 2, you will get the adjoining figure (iv). Now we have to find two points, R
and S, to complete the square PQRS. R should be on S
the perpendicular at Q and S on the perpendicular at P.
This can easily be done with the help of a compass.
Use a ruler to set the distance between the pointer of 6 cm
the compass to the pencil’s lead at 6 cm.
Step 3: Without changing the setting of the compass, P 6 cm Q P 6 cm Q
place the pointer at P and make an arc to cut the (iv) (v)
perpendicular at P at point ‘S’ as shown in the S R S R
figure (v).

Similarly, place the pointer at Q and make an arc to 6 cm 6 cm 6 cm 6 cm
cut this perpendicular at Q. Mark it ‘R’ as shown in the
figure (vi). 90° 90°
Step 4: Join SR with the help of a ruler and pencil to P 6 cm Q P 6 cm Q
(vi)
(vii)
get the desired square PQRS [figure (vii)].
Now, it is clear that PQ = PS = QR and ∠P = ∠Q = 90°.

How long is the side RS? Is RS = 6 cm?
Yes, it is.

What are the measures of ∠R and ∠S? Is ∠R = ∠S = 90°?
Yes, it is.
Therefore, PQRS is a square as it satisfies both the rules Note
S1 and S2.
Construction 6: Draw a rectangle having S 6 cm R Before starting any construction,
students are advised to draw its
sides 4 cm and 6 cm. After drawing, check Rough figure rough figure with all measurements
whether it satisfies the properties of a 4 cm marked. It always helps to construct
rectangle. (NCERT) P Q the required figure.

Playing with Constructions 225