Basic Geometrical Ideas
Question 1.
Classify the following curves as
(i) Open or
(ii) Closed.
Solution:
Open curves are (a) and (c) and closed curves are (b), (d) and (e).
Question 2.
Draw rough diagrams to illustrate the following:
(a) Open curve
(b) Closed curve
Solution:
Rough diagram to illustrate
(a) Open curve is
(b) Closed curve is
Question 3.
Draw any polygon and shade its interior.
Solution:
We know that in a closed curve, the interior is inside of the curve. Thus, shaded portion of the polygon indicate its interior.
Question 4.
Consider the given figure and answer the questions:
(a) Is it a curve?
(b) Is it closed?
Solution:
(a) Yes, the given figure represents a curve.
(b) Yes, the curve is closed.
Question 5.
Illustrate, if possible, each one of the following with a rough diagram:
(a) A closed curve that is not a polygon.
(b) An open curve made up entirely of line segments.
(c) A polygon with two sides.
Solution:
(a) Impossible, as a close plane figure bounded by lines is called a polygon.
(b) No, impossible, as a polygon of two sides cannot be drawn.
(c) Yes, it may be as
