# NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals The chapter likewise covers various polygons and contains four exercises which help the students in understanding these shapes appropriately. The arrangement of quadrilaterals is dependent on the nature of its sides or angles:

Polygons
A closed curve consisting of only line segments is called a polygon. The sides of a polygon never cross each other.

Classification of Polygons based on the Number of Sides

• Triangle - 3 sides
• Pentagon – 5 sides
• Hexagon – 6 sides
• Heptagon – 7 sides
• Octagon - 8 sides
• Nonagon - 9 sides
• Decagon - 10 sides

Diagonals
Diagonals are the line segments connecting two non-consecutive vertices of a polygon.

Polygons based on Shape

• A concave polygon has one of its interior angles greater than 90°
• A convex polygon is the one that has all its interior angles less than 180°.

Polygons based on Regularity

• A regular polygon has all the sides, and all the angles equal, i.e. a square.
• An irregular polygon is neither equilateral nor equiangular, i.e. a rectangle.

The sum of all the inner angles of a polygon equals to [(n−2) ×180°], where n refers to the number of sides. The sum of all the external angles of a polygon equals to 360°.

Parallelogram

• A parallelogram has four sides and four angles.
• Also, the opposite sides and opposite angles of a parallelogram are equal.
• Opposite angles in a parallelogram are equal.
• Adjacent angles in a parallelogram are supplementary.
• The diagonals of a parallelogram are known to bisect each other at the point of intersection.