# Quadrilaterals

## Exercise 3.1 Part 1

Question 1: Given here are some figures.

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

**Solution:**

(a) Simple curve: 1, 2, 5, 6, 7

(b) Simple closed curve: 1, 2, 5, 6, 7

(c) Polygon: 1, 2

(d) Convex polygon: 2

(e) Concave polygon: 1

Question 2: How many diagonals does each of the following have?

(a) A convex quadrilateral

(b) A regular hexagon

(c) A triangle

**Solution:** (a) Two, (b) 9, (c) 0 (zero)

Question 3: What is the sum of the measures of the angles of a convex quadrilateral? Why this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try!)

**Solution:**Solution: Angle sum of a convex quadrilateral `= (4 – 2) xx 180⁰ = 2 xx 180⁰ = 360⁰`

Since, quadrilateral, which is not convex, i.e. concave has same number of sides i.e. 4 as a convex quadrilateral have, thus, a quadrilateral which not convex also hold this property. i.e. angle some of a concave quadrilateral is also equal to 360⁰

Question 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

**Solution:** Given number of sides = 7

Angle sum of a polygon with 7 sides `= (7 – 2) xx 180⁰ = 5 xx 180⁰ = 900⁰`

(b) 8

**Solution:** Given number of sides = 8

Angle sum of a polygon with 8 sides `= (8 – 2) xx 180⁰ = 6 xx 180⁰ = 1080⁰`

(c) 10

**Solution:** Given number of sides = 10

Angle sum of a polygon with 10 sides `= (10 – 2) xx 180⁰ = 8 xx 180⁰ = 1440⁰`

(d) n

**Solution:** Given number of sides = n

Angle sum of a polygon with n sides `= (n – 2) xx 180⁰ = (n – 2)180⁰`

Question 5: What is a regular polygon?

State the name of a regular polygon of (i) 3 sides (ii) 4 sides (iii) 6 sides

**Solution:** A polygon with equal sides and equal angles is called reagular polygon.

(i) Equilateral triangle

(ii) Square

(iii) Regular hexagon