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GEOMETRY-LINES AND ANGLES
GEOMETRY- LINES AND ANGLES
Basic Geometrical Concepts
Point: A fine dot marked with a sharp edged pencil represents a point. It has no length, breadth and thickness. Points are denoted by capital letters like A,B,C etc., Geometrically a point is an undefined term.
Dimension of Point: A point has no dimensions point has no thickness or size, generally we should keep a dot as thin as possible to represent a point.
Example: A person travelling along a straight path from Miyapur to Chintal, can be represented diagramatically as the first dot on the line named as point ‘T’ represnts Miyapur, the second dot ‘P’ represents a person and the third dot name as ‘H’ represents Chintal
Line: Mark two points A and B on a plain white paper and join them with the help of a ruler and pencil you get the adjoint figure
This line segment AB is formed by joining the two points A and B. That means this has two end points.
Observe the two adjacent figures:
by extending the line, segment \(\overleftrightarrow {AB}\) on either side figure (ii) is formed . We read this \(\overleftrightarrow {AB}\) as “line AB” simply a line segment extended endlesly in both the directions is called a “line”. Some times a line is represented by a small letter l,m,n,....etc.,
Collinear Points: The points lying on the same line are called collinear points.
Example: If \(\overline {AB} \)= 3cm, \(\overline {BC} \)=4cm, the length of \(\overline {AC} \) must be 7cm
That means \(\overline {AB} +\overline {BC} =\overline {AC} \),
Therefore point ‘B’ must be in between A and C such points are called collinear points.
Note: 1) A Line has no end points
2) A line contains infinite number of points
3) A line has length but no thickness.
4) The line segment is a part of line
Example: Four points A,B,C, and D are marked on the following line
Here the points A,B,C,&D are lying on the same line or the line is passing through these points .Hence A,B,C, and D are called Collinear points.
Non-Collinear Points:
The points which do not lie on the same line are called Non-Collinear Points
Note: Number of lines that can be draw through ‘n’ Non–Collinear points is \(\frac{{n\left( {n - 1} \right)}}{2}\) -
GEOMETRY- LINES AND ANGLES
GEOMETRY- LINES AND ANGLES
Basic Geometrical Concepts
Plane: In mathematics, a smooth flat surface which extends endlessly in all the directions is called a “Plane”
Example: 1. Surface of a black board in your class room.
2. Floor of the class room etc
Note: 1.A plane has length and breadth
2. A plane has no thickness or boundary
3.An infinite number of lines can be drawn to pass through a given point in a plane
4. There is one and only one line that can be drawn to pass through two given points in a plane and this line lies wholly in the plane.
5.Two lines lying in a plane either intersect exactly at one point or are paralle
Plane Figures: The figures drawn in a plane with flat surfaces are called plane figures
Example: Triangle, Rectangle, Circle ....etc.,
Incidence Properties in a Plane:
1) Points belonging to the same plane are called co–planar Points.
2) Lines belonging to the same plane are called as Co-Planar Lines
3) Only one line can be drawn through two different points in a plane. The line wholly lies in the plane containing the two points. But we can drawn infinite curved lines through two points in a plane .
4) Two different lines in a plane having a common point are called intersecting lines.Two intersecting lines in a plane have only one common point and the common point of intersecting lines is also called as point of intersection.
5)An unlimited number of lines can be drawn through a given point in a plane and they are called as concurrent lines and the point through which they pass is called as point of concurrence (or) Simply if three or more lines intersects at only one point , then such lines are called concurrent lines
Space:
The portion enclosed by an infinitly large ball is called space. It is a set of infinite points.
Note: 1. Two straight lines can not enclose a space
2. A space contains an infinite numbr of planes.
3. Points, lines and planes are subsets of space.
4. A space has infinte length, breadth and also thickness.