Understanding quadrilaterals chapter3 grade 8 cbse

UNDERSTANDING QUADRILATERALS

CURVES A plane curve is a curve that lies in a single plane or a plane

surface like paper. A plane curve may be closed or open.

POLYGONS

Polygon is a closed plane figure bounded by three or more straight sides that meet in pairs in the same number of vertices, and do not intersect other than at these vertices.

PARTS OF A POLYGON

- The endpoints of the sides of polygons are called vertices. When naming a polygon, its vertices are named in consecutive order either clockwise or counterclockwise.

- Consecutive sides are two sides that have an endpoint in common. The four-sided polygon in Figure below could have been named ABCD, BCDA, or ADCB, for example. It does not matter with which letter you begin as long as the vertices are named consecutively. Sides AB and BC are examples of consecutive sides.

There are four pairs of consecutive sides in this polygon.

PARTS OF A POLYGON A diagonal of a polygon is any segment that joins two

nonconsecutive vertices. Figure shows five-sided polygon QRSTU. Segments QS , SU , UR , RT and QT are the diagonals in this polygon.

Diagonals of a polygon can be found with the formula given

below :

CLASSIFICATION OF POLYGONS

Polygons first fit into two general categories— convex and not convex (sometimes called concave). A polygon is concave if there are two points somewhere inside it for which a segment with these as its endpoints cuts at least 2 of the sides of the polygon.A polygon that is not concave is called convex

CLASSIFICATION OF POLYGONS

CLASSIFICATION OF POLYGONS

Polygons are also classified by how many sides (or angles or vertices) they have. The following lists the different types of polygons and the number of sides that they have:

A triangle is a three-sided polygonA quadrilateral is a four-sided polygon. A pentagon is a five-sided polygon. A hexagon is a six-sided polygon. A septagon or heptagon is a seven-sided polygon. An octagon is an eight-sided polygon. A nonagon is a nine-sided polygon. A decagon is a ten-sided polygon

REGULAR POLYGONS

When a polygon is both equilateral and equiangular, it is referred to as a regular polygon. For a polygon to be regular, it must also be convex.

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SUM OF INTERIOR ANGLES OF POLYGON

Sum of the interior angles of a polygon = (N - 2) x 180°Note: Sum of exterior angles of any polygon is always 360 degrees & the sum of interior angles of a polygon can be more or less than 360 degrees which can be calculated by the formula given above.

A Quadrilateral is any shape with 4 sides . The word “quadrilateral” comes from two Latin words “quadri” which means ‘a variant of four’ and “lateral” which means side.

PROPERTIES: with four sides with four angles with four vertices With one pair of diagonals

QUADRILATERALS

Interior Angle Sum Property: According to this property, the sum of the interior angles of the quadrilateral is 360°

Exterior Angle Sum Property: According to this property, the sum of the exterior angles of the quadrilateral is 360°

QUADRILATERALS

Quadrilaterals

Rectangle

Parallelogram

Rhombus

Square

IsoscelesTrapezoid

Kite

Quadrilateral(Trapezium)

Trapezoid

Types of Quadrilaterals

RECTANGLE

means "right angle"

and show

equal sides

Opposite sides are parallel and congruent . The diagonals bisect each other. The diagonals are congruent.

A rectangle is a four-sided shape where every angle is a right angle (90°).

RHOMBUS

A rhombus is a four-sided shape where all sides have equal length.

Also opposite sides are parallel and opposite angles are equal. Another interesting thing is that the diagonals (dashed lines in second figure) of a rhombus bisect each other at right angles.

SQUARE

means "right angle"

show equal sides

A square has equal sides and every angle is a right angle (90°)A square can be thought of as a special case of other

quadrilaterals, for example: a rectangle but with adjacent sides equal a parallelogram but with adjacent sides equal and the angles all 90° a rhombus but with angles all 90°

PARALLELOGRAM

A parallelogram is a quadrilateral with opposite sides parallel. Also opposite angles are equal (angles "a“ is same as angles "b“ ). The opposite sides are equal .The adjacent angles are supplementary and the diagonals bisects each other ; but they are not equal.It is the "parent" of some other quadrilaterals,

which are obtained by adding restrictions of various kinds: A rectangle is a parallelogram but with all four interior angles fixed at 90°. A rhombus is a parallelogram but with all sides equal in length. A square is a parallelogram but with all sides equal in length and all angles fixed at 90°.

TRAPEZIUM

Trapezoid Isosceles Trapezoid

A trapezium is quadrilateral which has at least one pair of parallel sides It is called an Isosceles trapezium if the sides that aren't parallel are equal in length and both angles coming from a parallel side are equalNote : Trapezium is UK terminology & in US terminology it is called as Trapezoid

KITE

Two pairs of adjacent sides of a kite are equal in length One pair of opposite angles (the ones that are between the sides of unequal length) are equal in size. One diagonal bisects the other. Diagonals intersect at right angles.

A kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other.Kite quadrilaterals are named for the wind-blown, flying kites, which often have this shape 

QUADRILATERALS

Green House

(by Wasim Ahmed VIII-B9)