# How many diagonals does each of the following have?

(a) A convex quadrilateral

(b) A regular hexagon

(c) A triangle

**Solution:**

A diagonal is a line segment connecting two non-consecutive vertices of a polygon.

Draw the given polygon and mark the vertices and then, draw lines joining the two nonconsecutive vertices. From this, we can calculate the number of diagonals.

(a) Convex quadrilateral - 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.

**Video Solution:**

## How many diagonals does each of the following have? (a) A convex quadrilateral (b) A regular hexagon (c) A triangle

### NCERT Solutions Class 8 Maths - Chapter 3 Exercise 3.1 Question 2

**Summary:**

(a) The number of diagonals a convex quadrilateral has is 2. (b) The number of diagonals a regular hexagon has is 9. (c) The number of diagonals a triangle has is 0.