Exercise 4.2

1. Classify the following curves as (i) Open or (ii) Closed.

Remember:
• Open curve: Starts and ends at different points.
• Closed curve: Starts and ends at the same point (forms a loop).

Curve (a)
Classification:
(a) Open curve
(b) Closed curve
(c) Open curve
(d) Closed curve
(e) Closed curve
2. Draw rough diagrams to illustrate the following:
(a) Open curve
Open curve example
(b) Closed curve
Closed curve example
3. Draw any polygon and shade its interior.
Shaded polygon
(a shaded triangle)

A polygon is a closed curve made of only line segments.
Its interior is the area inside the boundary.

4. Consider the given figure and answer the questions: (a) Is it a curve? (b) Is it closed?
Given figure for Q4
(a) Yes, it is a curve (any drawing without lifting the pencil is a curve).
(b) Yes, it is closed (starts and ends at the same point).
5. Illustrate, if possible, each one of the following with a rough diagram:
(a) A closed curve that is not a polygon
Closed non-polygon curve
(smooth, no line segments)
(b) An open curve made up entirely of line segments
Open curve of line segments
(any zigzah letter )
(c) A polygon with two sides

This is not possible.
A polygon must have at least 3 sides (triangle is the smallest polygon).

Reason: Two line segments cannot form a closed shape.