Page 158 - ICSE Math 6

Interior, exterior and boundary of closed figures

In the given figure, point ‘P’ lies inside the curve, point ‘Q’ lies
outside the curve and point ‘R’ lies on the boundary of the curve.
Thus, a closed curve divides the plane into three parts. They are; P
(a) Interior of the closed curve: It is the set of all points lying R Q
inside the curve.
(b) Exterior of the closed curve: It is the set of all points lying outside the curve.

(c) Boundary of the closed curve: It is the set of all points lying on the closed curve.
We can also say that the interior of a curve is simply the area inside the curve and exterior is the area
outside the curve.

The interior of a closed curve together with its boundary is called its region.

Curvilinear and linear boundaries
A boundary having only curved lines is known as a curvilinear boundary.

Curvilinear
boundary

A boundary having only line segments is known as a linear boundary.

Linear boundary

EXERCISE 14.1

1. Write True or False.
(a) A point has definite length.
(b) A line has indefinite length and definite breadth.
(c) A ray has one end point.
(d) A line segment has two end points and definite length.
(e) The distance between two parallel lines is always the same.
(f) Intersecting lines always meet at an angle of 90°.

2. How many end points are there in the following?
(a) ray (b) line segment (c) line
3. How many line segments are there in the following figures?

D C A F E D

(a) O (b) (c)
A B B D C A B C

4. Which of the following are closed figures?

(a) (b) (c) (d)

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