# Ex.3.1 Q2 Understanding Quadrilaterals Solution - NCERT Maths Class 8

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## Question

How many diagonals does each of the following have?

(b) A regular hexagon

(c) A triangle

## Text Solution

What is known?

Polygons with known number of vertices.

What is unknown?

Number of diagonals

Reasoning:

A diagonal is a line segment connecting two non-consecutive vertices of a polygon. Draw the above given polygon and mark vertices and then, draw lines joining the two non-consecutive vertices. From this, we can calculate the number of diagonals.

A convex quadrilateral has two diagonals. Here, $$AC$$ and $$BD$$ are two diagonals.

(b) A regular hexagon Here, the diagonals are $$AD, \,AE,\, BD,\, BE,\, FC,\, FB, \,AC,\, EC$$ and $$FD.$$ Totally there are $$9$$ diagonals.

(c) A triangle A triangle has no diagonal because there no two non-consecutive vertices.

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