Rectilinear Figure

What is rectilinear figure?

A plane figure whose boundaries are line segments is called a rectilinear figure. A rectilinear figure may be closed or open.

Polygon: A closed plane figures whose boundaries are line segments is called a polygon. The line segments are called its sides and intersection of consecutive sides is called a vertex. In general, a figure bounded by more than four line segments is called a polygon. A polygon is given a special name according to the number of sides it has.

For example:

1. Pentagon:

It’s a 5 sided polygon. The sides are PQ, QR, RS, ST and TP.

2. Hexagon:

It’s a 6 sided polygon. The sides are PQ, QR, RS, ST, TU and UP.

3. Heptagon:

It’s a 7 sided polygon. The sides are PQ, QR, RS, ST, TU, UV and VP.

4. Octagon:

It’s a 8 sided polygon. The sides are PQ, QR, RS, ST, TU, UV,VW and WP.

5. Nonagon:

It’s a 9 sided polygon. The sides are PQ, QR, RS, ST, TU, UV,VW, WX and XP.

5. Decagon:

It’s a 10 sided polygon. The sides are PQ, QR, RS, ST, TU, UV,VW, WX, XY and YP.

What is diagonal of a polygon?

A line segment joining any two consecutive vertices of a polygon is called a diagonal of a polygon.

Here, the pentagon PQRST, the diagonals are PR, PS, QS, QT and RT.

Interior and exterior angles of a polygon:

The angle between any two consecutive sides of a polygon is called an interior angle of a polygon.

Here, QPT, PQR, QRS, RST and STP are the interior angles.

If one side of a polygon is produced, the angle of the extended side makes with the next side of the polygon is known as an exterior angle of the polygon. 

Here, APQ, BQR, CRS, DST and ETP are the exterior angles.

At every vertex, the interior angle and the exterior angle form a linear pair, i.e., the sum of the interior angle and the exterior angle equals 180 degree. For example, QPT + APQ = 180°.

Convex polygon:

If the interior angles of a polygon are less than 180 degree, the polygon is known as convex polygon.

Here, PQRSTU is a convex hexagon.

Non convex polygon:

If atleast one interior angle of a polygon is more than 180 degree, the polygon is known as a non convex polygon. 

Here, PQRSTUV is a non convex heptagon as reflex TUV  180°.

Equilateral polygon:

A polygon whose all sides are equal is called an equilateral polygon.

Equiangular polygon:

A polygon whose all angles are equal is called an equiangular polygon.

Regular polygon:

A polygon whose all sides and all angles are equal is called a regular polygon.

9th Grade Math

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