Lines and angles Class 9 _CBSE

Lines and angles Class 9
it is based on the CBSE syllabus

1. Lines And Angles
Class-9
Done By : Smrithi Jaya

2. Types of lines

▪Line
a line can be defined as a straight one-
dimensional figure that has no thickness and
extends endlessly in both directions
Line Segment
A line segment can be defined as a line with 2
end points
Ray
A ray can be defined as a line with one end
point

▪Collinear points : points that lie on the same
line
Non collinear points : points that do not lie on
tha same line

3. Angles
▪When two rays originate from the same end point
an angle is formed.
▪The rays are called arms and the endpoint is called
vertex

4. Types of Angles
▪Acute Angle - 0°−90°
▪Obtuse Angle - 90°−180°
▪Right Angle - 90°
▪Straight angle - 180°
▪Complete angle - 360°
▪Reflex angle - 180°−360°


In the given figure :

�=??????????????????° �.� � �� ��� ���??????�� ????????????�??????�

�=?????????????????? −�=?????????????????? −??????????????????=????????????°

5. Types of Angles

6. Adjacent angles
▪Two angles are said to
be adjacent if they
have
▪A common vertex
▪A common arm
▪Two non common
arms on different
sides of the common
arm

•Point B is the common
vertex
•BD is the common arm
•BA and BC are non-
common arms
•Therefore
<1 &#3627408470;&#3627408480; ??????&#3627408465;&#3627408471;??????&#3627408464;&#3627408466;&#3627408475;&#3627408481; &#3627408481;&#3627408476; <2

7. Complementary and
supplementary angles
▪Complementary
angles
▪Two angles whose
sum is 90° are called
complementary
angles

▪Supplementary Angles
▪Two angles whose
sum is 180° are called
supplementary angles

8. Linear pairs and vertically
opposite angles
▪Linear pair property or
staraight line property


▪Vertically opposite
angles

If AC is a straight line,
then &#3627408485;+&#3627408486; = 180° or
<&#3627408436;&#3627408437;&#3627408439; and <&#3627408438;&#3627408437;&#3627408439; is a
linear pair
When AB and CD intersect
at O two pairs of vertically
opposite angles are formed
and are equal
i.e. <1= <2
<3= <4

9. Intersecting and
Non-intersecting lines
In this figure PQ and RS are
Intersecting lines
PQ and RS are parallel or
non - intersecting lines

10. Parallel lines and
transversal

11. Axioms and Theorems

AXIOMS


THEOREMS

The axiom is a statement which is self
evident

theorem is a statement which is not
self evident

Axiom cannot be proven by any kind of
mathematical representation.

Theorem can be proved by
mathematical representation

12. AXIOMS
▪Axiom 6.1 : if ray stands on a line the sum of two
angles formed is 180°
▪&#3627408485;+&#3627408486;=180°


▪Axiom 6.2 : if sum of two angles is 180° then the
two non common arms form a line
▪i.e AC is a line

13. AXIOMS
▪Axiom 6.3 or corresponding angles axiom: if a
transversal intersects two parallel lines, then each
pair of corresponding angles is equal.
i.e. <1=<5 ,<2= <6 ,<3= <7, <4=<8



Axiom 6.4 : If a transversal intersects two
lines such that angles formed are corresponding then
the two lines are said to be parallel.

14. THEOREMS
▪Theorem 1 : vertically opposite angles are
congruent
▪Theorem 2: if a transversal intersects two parallel
lines , then each pair of alternate interior angles
are equal
▪Theorem 3 : If a transversal intersects two parallel
lines such that a pair of alternate interior angles is
equal then the two lines are parallel.
▪Theorem 4 : If a transversal intersects two parallel
lines then each pair of co-interior angles are
supplementary.

15. THEOREMS
▪Theorem 5 : If a transversal intersects two parallel
lines such that a pair of co interior angles are
supplementary then the two lines are parallel.
▪Theorem 6 : Lines which are parallel to the same
line are parallel to each other.
▪Theorem 7: The sum of the angles of a triangle is
180°.
▪Theorem 8 or Exterior angle theorem : If a side of a
triangle is produced then the exterior angle so
formed is equal to sum of interior opposite angles.

16. Done By:
Smrithi Jaya