How many diagonals does each of the following have? A. A convex quadrilateral B. A regular hexagon C. A triangle

NCERT - Mathematics

Book: NCERT - Mathematics

Chapter: 3. Understanding Quadrilaterals

Subject: Maths - Class 8^th

Q. No. 2 of Exercises 3.1

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2

How many diagonals does each of the following have?
A. A convex quadrilateral

B. A regular hexagon

C. A triangle

(a) There are 2 diagonals in a convex quadrilateral.(See in figure below)

(b) There are 9 diagonals in a regular hexagon

(Represented in figure)

(c) A triangle does not have any diagonal in it

(Represented in figure)

4

Chapter Exercises

Exercises 3.1

Exercises 3.2

Exercises 3.3

Exercises 3.4

1

Given here are some figures
(1) (2)

(3) (4)

(5) (6)

(7) (8)

Classify each of them on the basis of the following:

A. Simple curve

B. Simple closed curve

C. Polygon

D. Convex polygon

E. Concave polygon

2

How many diagonals does each of the following have?
A. A convex quadrilateral

B. A regular hexagon

C. A triangle

3

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!)

4

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

5

What is a regular polygon?
State the name of a regular polygon of

(i) 3 sides

(ii) 4 sides

(iii) 6 sides

6

Find the angle measure x in the following figures
A.

B.

C.

D.

7

A. Find x + y + z

B. Find x + y + z + w