Understanding Quadrilaterals - Maths Class 8th - Ex 3.1 - Q4 - Chapter 3 - NCERT - CBSE
Understanding Quadrilaterals - Maths Class 8th - Ex 3.1 - Question 4 - Chapter 3 - NCERT - CBSE
Full exercise on Understanding Quadrilaterals, fully solved. This is a video tutorial for 8th class NCERT CBSE students. For other educational stuff, subscribe and press bell icon.
Introduction
You know that the paper is a model for a plane surface. When you join a number of points without lifting a pencil from the paper (and without retracing any portion of the drawing other than single points), you get a plane curve.
Polygons
A simple closed curve made up of only line segments is called a polygon.
Classification of polygons
We classify polygons according to the number of sides (or vertices) they have. Triangle,Quadrilateral,Pentagon,Hexagon,Heptagon,Octagon,Nonagon,Decagon and n-gon.
Diagonals
Adiagonalis a line segment connecting two non-consecutive vertices of a polygon.
Convex and concave polygons
Can you find how these types of polygons differ from one another? Polygons that are convex have no portions of their diagonals in their exteriors.
Regular and irregular polygons
A regular polygon is both ‘equiangular’and ‘equilateral’. For example, a square has sides of equal length and angles of equal measure. Hence it is a regular polygon. A rectangle is equiangular but not equilateral. Is a rectangle a regular polygon? Is an equilateral triangle a regular polygon? Why?
Angle sum property
Do you remember the angle-sum property of a triangle? The sum of the measures of the three angles of a triangle is 180°. Recall the methods by which we tried to visualise this fact. We now extend these ideas to a quadrilateral.
EXERCISE 3.1
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
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
7. (a) Find x + y + z (b) Find x + y + z + w
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