Download Class 8: Lines and Angles (Lecture Notes) – Part 1

Class 8: Lines and Angles (Lecture Notes)
– Part 1
Basic Geometrical Concepts
1. Axioms: The basic facts that are taken for granted, without mathematical proof, are called
Axioms. Therefore, the axiom can be used as the premise or starting point for further
reasoning or arguments, usually in logic or in mathematics.
Example: A line is composed of infinite points. The halves of equals are equal.
2. Statement: A statement (or proposition) is a sentence that is either true or false (both not
both).
Example: '5 is an odd integer' is a statement. But ‘11 is a cool number' is not a
(mathematical) statement. The sum of the angles of a triangle is 180 degree is a true
statement.
3. Theorem: A statement that requires a proof is called Theorem. A theorem can also be
defined as a statement that has been proved on the basis of previously established
statements, such as other theorems—and generally accepted statements, such as axioms.
A theorem is a logical consequence of the axioms.
Example: The Pythagoras Theorem (𝑎2 + 𝑏 2 = 𝑐 2 )
Fundamental Geometrical Terms
Point: An entity that has a location in space or on a plane, but has no extent. In simple
term it is like a fine dot denoted by capital
letter A, B C etc.
2. Line Segment: A line segment is a part of
a line that is bounded by two distinct
end points, and contains every point on the
line between its endpoints A and B. The A
and B are called its end points. The line
segment has a definite length. Line segment
̅̅̅̅.
is denoted by 𝐴𝐵
3. Ray: A line segment AB when extended
infinitely in one direction is called a Ray and is denoted by ⃗⃗⃗⃗⃗
𝐴𝐵 . A ray only has one end
point A. A ray does not have definite length.
1.
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4.
Line: A line segment AB when extended infinitely on both sides is called a line and is
⃡⃗⃗⃗⃗ . Off course it does not have end points and no definite length. Line can
denoted by 𝐴𝐵
be represented by small letters like l, m, n etc.
Incidence Axioms on Lines
1. A line contains infinite number of points
2. Infinite number of lines can be drawn through one point
3. Only one line can be drawn through two given point A and B
Collinear Points
A set of three or more points are called collinear if one line can be drawn through all of them.
Plane
It is a flat surface (two dimensional surface) that extends infinitely in
all four directions.
Intersecting lines
Two lines that have a common point are said to be intersecting lines.
The common point of the two intersecting lines is call point of
intersection.
Concurrent Lines
Three of more lines in a plane are said to be concurrent if they all
intersect at one point
Parallel Lines
Two lines in a plane are said to be parallel if they do not have
any point in common. There lines (say l and m) are denoted
as l ||m.
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