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.
☛ Check: NCERT Solutions for Class 8 Maths Chapter 3
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.
☛ Related Questions:
- What is the sum of the measures of the angles of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try!)
- Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.) What can you say about the angle sum of a convex polygon with number of sides? (a) 7 (b) 8 (c) 10 (d) n
- What is a regular polygon? State the name of a regular polygon of (i) 3 sides (ii) 4 sides (iii) 6 sides
- Find the angle measure x in the following figures: