Presented by Srashti Nagori

Class 8th

Section B

Roll No 26

Geometry starts with a point which is dimensions. A point has no length, no breadth and no height.

o

A

CB

D

Two straight lines either intersect or are parallel

If two lines intersect, they have only one point of intersection;

for example, AB and CD intersect at a point.

A four sided plane figure is called a quadrilateral

D C

BA

If we join four non-collinear points A,B,C,D, taken two at a time, we get six different lines through them namely AB, BC, CD, DA, AC and BD. The first four enclose a quadrilateral ABCD and the remaining two make its two diagonals.

A quadrilateral has four vertices, four sides and two diagonals.

Convex quadrilateral and Concave quadrilateral

In convex quadrilateral, both the diagonals lie in the interior of the quadrilateral.

In a convex quadrilateral, line segment joining any two points lying in its interior region completely lies in the quadrilateral.

In convex quadrilateral, both diagonals intersect inside the quadrilateral.

If in a quadrilateral, any one side is produced and the quadrilateral completely lies one side of it, then the quadrilateral is convex.

Convex quadrilateral

If a quadrilateral contains any one side such that when it is produced, the quadrilateral does not wholly lie on one of its sides, i.e., a part of it lies on the opposite side of the produced side, then the quadrilateral is said to be concave.

Concave quadrilateral

In a concave quadrilateral, two of the sides are such that when they are produced, they divide the interior of the quadrilateral in two parts.

In concave quadrilaterals, one diagonal lies in the interior and the other lies in the exterior of the quadrilateral.

Properties of angles of a quadrilateral(i) In a convex quadrilateral, all the four angles are less than

180 degree.

(ii) In a concave quadrilateral, one of the angles lies between 180 degree and 360 degree.

(iii)Sum of all the angles of a quadrilateral is 360 degree.

Closed figureWhen three lines intersect at three different points, they enclose a closed figure called triangle.

A closed figure formed by four straight lines intersecting at four different points is called a quadrilateral.

A four sided plane figure with no set pattern is simply called a quadrilateral. Some special quadrilateral are:

Parallelogram

A quadrilateral with two pairs of opposite sides parallel is called a parallelogram.

Rhombus

A parallelogram with all sides equal is called rhombus.

Rectangle

A parallelogram with one angle measuring 90 degree is called a rectangle. (The other three angles will also be 90 degree each).

Square

A rhombus with one angle measuring 90 degree is called a square. (The other three angles will also be 90 degree each).

Trapezium

A quadrilateral with only pair of opposite sides parallel, is called a trapezium.

Kite

A quadrilateral with two pairs of adjacent sides equal is called a kite.

Angles of a quadrilateral

Four sides of a quadrilateral form four angles at their four

vertices. Four angles of the quadrilateral ABCD are <ABC,

<BAD, <BCD, <CDA. They can also be written as <A, <B,

<C, <D

Submitted to

Meeta ma’am

Maths teacher

Thank You!