Understanding Quadrilaterals Class 8 Notes Maths Chapter 3

Students can go through AP 8th Class Maths Notes Chapter 3 Understanding Quadrilaterals to understand and remember the concepts easily.

Class 8 Maths Chapter 3 Notes Understanding Quadrilaterals

Understanding Quadrilaterals Class 8 Notes Maths Chapter 3 1

Understanding Quadrilaterals Class 8 Notes Maths Chapter 3

→ Plane surface : A plane is a flat, two dimensional surface that extends indefinitely. For more understanding : Space – 3 dimensional; Line – One dimensional;
Whereas a plane is the two – dimensional analogue of a point.

→ Plane curve : A curve that lies completely in a single plane. In other words when we join number of points without (break) lifting our pen from the paper, then the diagram is called Plane curve.
Ex : Understanding Quadrilaterals Class 8 Notes Maths Chapter 3 2

→ Curve : Any line (Straight or bended) is a curve.

→ Simple curve : A curve which does not cross (cut) itself is a simple curve.
Understanding Quadrilaterals Class 8 Notes Maths Chapter 3 3

→ Closed curve : A curve which has no open ends, is called closed curve.
Understanding Quadrilaterals Class 8 Notes Maths Chapter 3 4
These are closed curves.
Understanding Quadrilaterals Class 8 Notes Maths Chapter 3 5
These are not closed curves, because open ends (A,B) are there in curves.
Understanding Quadrilaterals Class 8 Notes Maths Chapter 3 6

Understanding Quadrilaterals Class 8 Notes Maths Chapter 3

→ POLYGONS : Polygons are simple closed curves made up of only line segments.
Look at the following :
Understanding Quadrilaterals Class 8 Notes Maths Chapter 3 7
Understanding Quadrilaterals Class 8 Notes Maths Chapter 3 8

→ Classification of polygons :
We classify polygons according to the number of sides (or vertices) they have.
Understanding Quadrilaterals Class 8 Notes Maths Chapter 3 9

→ Diagonal: A diagonal is a line segment joining two non-consecutive (adjacent) vertices of a polygon.
i) Can you draw diagonals in a triangle ?
Answer:
No, because every two other vertices are adjacent to the third one.

ii) Can you draw diagonals in a quadrilateral ?
Yes, we can draw 2 diagonals.
Understanding Quadrilaterals Class 8 Notes Maths Chapter 3 10

Understanding Quadrilaterals Class 8 Notes Maths Chapter 3

→ Interior / exterior of closed curve :
Understanding Quadrilaterals Class 8 Notes Maths Chapter 3 11
Interior has boundaries but exterior has no boundaries.

→ Convex Polygon : A polygon, that is the boundary of a convex set. (in other words). The line segment between two points of the polygon is contained in the union of the interior and the boundary of the polygon.
(or)
A polygon, each of its angles is less than 180°.
(or)
Polygons that are convex have no portions of their diagonals in their exteriors, (or) Any line segment joining any two different points in the interior of the polygon lies completely in its interior.
Ex : Understanding Quadrilaterals Class 8 Notes Maths Chapter 3 12

→ Concave Polygon : A polygon which has at least one reflex angle that means one of its interior angle is more than 180°.
(or)
Understanding Quadrilaterals Class 8 Notes Maths Chapter 3 13

Understanding Quadrilaterals Class 8 Notes Maths Chapter 3

→ Regular Polygon : A Polygon in which lengths of all sides are equal and all interior angles are equal.
That means a regular polygon is both ‘Equlangula? and ‘Equilateral’. Ex: Square.
A square is regular polygon, because all its angles are same (that are 90°) and ail sides are equal.
Understanding Quadrilaterals Class 8 Notes Maths Chapter 3 14
Because all its angles (60°) are equal and sides are also equal.
Is there a triangle that is equilateral but not equiangular ?
Answer:
No.

→ Angle Sum Property of a Triangle: Sum of all three angles of a triangle is equal to 180°.

→ Angle Sum Property of a Quadrilateral: Sum of all four interior angles of a quadrilateral is equel to 360°.

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