Page 243 - Ganit Kaushal

16. State whether the following statements are True (T) or False (F).

(a) With ruler and compass sets, we can bisect any given line segment.
(b) Only one perpendicular bisector can be drawn to a given line segment.
(c) It is possible to construct a four-sided figure in which all the angles are 90°and opposite sides
are not equal.

(d) It is possible to draw two bisectors of a given line.
(e) If a rectangle is rotated at an angle of 30°, it remains a rectangle.
(f) A protractor is divided into 360 parts, representing 1° each.

Assertion Reason Type Questions
A statement of assertion (A) is followed by a statement of reason (R). Choose the correct option out of the
choices given below for each question:
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.

1. Assertion (A): A compass alone is not sufficient to construct a perfect square.
Reason(R): A square requires straight lines and right angles, which a compass alone can’t create.
2. Assertion (A): The perpendicular bisector of a chord of any circle passes through its centre.

Reason(R): The diameter of a circle is twice its radius.
3. Assertion (A): In a square all four sides are equal.

Reason(R): Any geometrical shape with four equal sides is a square.
4. Assertion (A): A scale is enough to make a perfect rectangle.
Reason(R): A rectangle is made up of straight lines only.

Summary of the Chapter

• All the points on a circle are at the same distance from its centre. This distance is called the radius of
the circle.
• A compass is used to construct circles and parts of circles.
• A rough diagram is useful in planning the steps needed to construct a given figure.
• A rectangle can be constructed if the lengths of its sides are known or if one side and a diagonal are given.
• The following are the important points to be remembered while using the instruments for construction:

– Draw smooth and thin lines
– Mark points lightly
– Maintain instruments with tips, pointers and fine edges
– Keep two pencils in your geometry box — one for drawing lines and marking points, and the other
for using in the compass to draw arcs and circles

Playing with Constructions 241