basic geometry
DESCRIPTION
here is a ppt on geometrical figures and it gives details all about the different types of geometrical shapes and give many pictures and short definitions on them..... it is a really good power point presentation.......TRANSCRIPT
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.