Page 230 - Ganit Kaushal

Sol. To construct a rectangle ABCD as shown in the adjoining figure, follow the steps given D C

below: Rough
figure
Step 1: Draw a line AB of any arbitrary length using a ruler and pencil (see figure (i)).
Step 2: Draw a perpendicular to the line AB at the point B with the help of a protractor 30°

as shown in the previous constructions (see figure (ii)). 60°
A B
Step 3: Now, with the help of a protractor, raise a line at point A, making an angle of
60° with line AB. This will cut the perpendicular from B, at point C (see figure (iii)).

Step 4: We know that D lies on the perpendicular to the line AB at A. Draw a line through A
perpendicular to AB with the help of a protractor (see figure (iv)).

C C

Note
Now, ∠A is divided into two angles.
One measures 60°. The other angle
60° 60° must be 30° ( 90° – 60° = 30°).
A (i) B A (ii) B A (iii) B A (iv) B

Step 5: Now to find point D on the perpendicular drawn at A, we use the fact that opposite sides of a
rectangle are equal, this can be easily done with the help of a compass. Take a compass, put its pointer
at C and set the distance equal to CB in its legs as shown in figure (v).

Now, without changing the setting of the compass,

put the pointer at A and draw an arc that cuts the Note
perpendicular from A as shown in figure (vi). Mark this Point D can also be marked using the
fact that all the angles of a rectangle
point as D. are right angles. How will it be done?
Students are advised to explore it.
Step 6: Join DC with a ruler and pencil to get the desired

rectangle ABCD as shown in figure (vii).
C D C D C

30°

60° 60° 60°
A B A B A B
(v) (vi) (vii)
Now, based on the above construction, answer the following questions:

What are the measurements of ∠ACD and ∠ACB?

Is AD = BC and AB = DC?

Discuss your answers with your class teacher to check if you are right.

228 Mathematics-6