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`

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