Four

Three

We know that, the shortest distance between two points is called a line segment. The line segment joining two points A and B is denoted by \(\bar {AB}\) or \(\bar {BA}\). The line segment in the given figure are as follows:
(i)\(\bar {AB}\) (or \(\bar {BA}\) ) (ii) \(\bar {AC}\) (or \(\bar {CA}\))
Yes, from the figure, it is clear that point A is the end point of each line segment.

Five situations of a point in our daily life are as follow:
(i) Tip of an ice cone.
(ii) An edge of a table.
(iii) Corner of a room.
(iv) Corner of a desk.
(v) Corner of a paper.

ABCD is a polygon, where interior is shaded as given below:

The curve given below is a closed curve, since its ends are joined:

No Point (0)

(a) Infinite number of lines can pass through one given point.
Let there be a point O on a surface.
Now, we can draw infinite lines through it.

(b) Exactly one and only one line can pass through two given points (say A and B)

We know that, a line is a line segment which can extend indefinitely in both directions. Name oflines in all possible ways are as follow:
(i) By taking A, all possible ways are \(\overleftrightarrow { AB } ,\overleftrightarrow { AC } and\overleftrightarrow { AD } \).
(ii) By taking B, all possible ways are \(\overleftrightarrow { BC } ,\overleftrightarrow { BD } and\overleftrightarrow {BA } \).
(iii) By taking C, all possible ways are \(\overleftrightarrow { CD } ,\overleftrightarrow { CA } and\overleftrightarrow {CB } \).
(iv) By taking D, all possible ways are \(\overleftrightarrow { DA } ,\overleftrightarrow { DB } and\overleftrightarrow {DC } \).

A rough sketch of a quadrilateral KLMN is given here

Now, from the above figure,
(a) KL,MN and LM,NK are two pairs of opposite sides.
(b) \(\angle K,\angle M\ and \angle L,\angle N\) are two pairs of opposite angles.
(c) KL, LM and LM, MN are two pairs of adjacent sides, because end point of one line is starting point of another line.
(d) Two angles are called adjacent angles, if they have common vertex. Hence, \(\angle K,\angle L\ and \angle L,\angle M\) are two pairs of adjacent angles because they have the common vertex L.

Seven sides i.e AB, BC, CD, DE, EF, FG, AG.

We know that, if a closed simple figure is made up entirely of line segments, then it is called a polygon.
(i) Polygon with five matchsticks.

(ii) Polygon with four matchstick

(iii) Polygon with three matchsticks

(iv) We know that, a polygon is a closed plane figure, bounded by line segments. So, with the help of two matchsticks, it is not possible to make a closed plane figure. Hence, no polygon is formed by two matchsticks.