basic geometry

BASIC GEOMETRICAL IDEAS

(2D)

INTRODUCTION

Geometry is the part of maths that deals with objects like points, lines, planes and space.

E.g. triangle, rectangle , circle etc.

Points Points are exact locations in space

and are named using capital letters. They are shown by small dots.

To name a point A point is designated by a capital letter

which is written next to the dot which represents it.

Thus points shown here will be referred to as point A, point B ,point C .

Line The representation of a line has only length and no

width or thickness .A line has no end points. A line extends infinitely in both directions.A few facts about lineThere are an unlimited number of points on a line.

There are an unlimited number of lines through a point.

Two lines can intersect in only one point

Exactly one line passes through two points.

plane

A plane can be thought of as a flat surface . Our desktop, the floor and classroom are models of planes. A plane extends without limit in all directions. There are three types-:

1.vertical 2.horizontal 3.parallel linesVertical and horizontal lines . e.g.. front wall of the

classroom

Parallel lines . E.g.

ray A ray has one end point and extends

without limit in one direction from the end point.

E.g. a light torch gives rays of light, the sun emanates the rays of light.

Line segments

A line segment is a portion of a line with two fixed end points.

Fact The shortest path connecting

two points is along the line segment.

Plane figure

In geometry , any collection of points is called a figure.

If all the points in a figure are in one place , the figure is a plane figure.

Open and closed figures

Closed figure-:A closed figure that does not intersect itself.

Open figures-:an opened figure that does intersect itself.

angle An angle is made up of two rays that

have the same end point. The end point at which the two rays meet is called the vertex of the angle. Each of the rays that form the angle are called the arms of the angle. The size of an angle depends on the rotation up to the terminal side. The amount of this rotation is called the measure of the angle.

Naming an angle

An angle can be named in three ways-:

1. With three letters2. With one letter3. With numerals or a small letter

Interior and exterior of an angle

Like any plane figure , an angle divides the plane in which it lies into two parts. One part is called the interior of angle and other exterior of angle. Interior tells about the inside of the figure and the exterior , tells the outside of the figure.

Triangles A triangle is a simple closed figure made of

three line segments.

Parts of a triangleA triangle six parts or six elements-:1. Three sides : AB , BC , CA2. Three angles : L BAC , L ABC , L CBA

MEDIANS OF A TRIANGLE

A line segment joining a vertex to the mid-point of the

side opposite to the vertex is called a meridian of a

triangle.ALTITUDES OF A TRIANGLES

An altitude of a triangle is the perpendicular drawn from a vertex to the opposite side.

Quadrilaterals

The figure made up of four line segments is called a quadrilateral . The points ABCD are called its vertices.

Sides , angles & diagonals

The four line segments AB , BC , CD & DA are called its sides.

The four angles L DAB ,L ABC ,L BCD , L CDA are called its angles.

The line segment joining two non-consecutive vertices is called a diagonal . E.g. AB and BD

Adjacent sides and opposite sides

1.Two sides of a quadrilateral are said to be adjacent sides .if they have a common end point.

2.Two sides of a quadrilateral are said to be opposite sides.

Adjacent angles and opposite angles1.Two angles of a quadrilateral are said to be

adjacent angles

2.Two angles of a quadrilateral are said to be opposite angles

CircleOne of the most important and familiar

figure is the circle .we come across hundreds of circles in a day

A circle is a simple closed curve all of whose points are at the same distance from a given point O in the same plane .the given point O is called the centre of the circle.

Parts of a circle

Radius -:a line segment joining the centre of

a circle to any point.

Chord -: a line segment joining any two parts

On a circle

Diameter -: a chord that passes through the

circle

Circumference -:the distance around a circle

Interior and exterior of a circle

The interior of a circle contains all the points in the plane whose distance from the centre is less than the radius

The exterior of a circle contains all the points in the place whose distance from the centre is greater than the radius.

Few more definitions Secant -: a line which intersects the circle at two distinct points

Arc. -: a part (continuous) of a circle

Semicircle -: a diameter divides a circle into two equal parts

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Segment -: a chord of a circle that divides the area enclosed by it into two parts

Sector -: the part of the circle enclosed by any two radii of the circle

Concentric circle -: two or more circles drawn with the same centre.