DIGITAL LIBRARY OF GLT SARAWATI BAL MANDIR, NEHRU NAGAR, BY DEEPESH SINGH CLASS 9th - F

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सूययशसध्दान्त: १२८

6. Point
An exact location on a plane is
called a point.
Line
Line
segment
Ray
A straight path on a plane,
extending in both directions
with no endpoints, is called a
line.
A part of a line that has two
endpoints and thus has a
definite length is called a line
segment.
A line segment extended
indefinitely in one direction
is called a ray.

7. RAY: A part of a line, with one endpoint, that continues
without end in one direction
LINE: A straight path extending in both directions with no
endpoints
LINE SEGMENT: A part of a line that includes two
points, called endpoints, and all the points between
them

8. INTERSECTING LINES: Lines that cross
PARALLEL LINES: Lines that never cross and are always
the same distance apart

9. Common
endpoint
B C
B
A
Ray BC
Ray BA
Ray BA and BC are two non-collinear rays
When two non-collinear rays join with a common endpoint
(origin) an angle is formed.
Common endpoint is called the vertex of the angle. B is the
vertex of ABC.
Ray BA and ray BC are called the arms of ABC.

10. An angle divides the points on the plane into three regions:
A
B
C
F
R
P
T
X
• Points lying on the angle
(An angle)
• Points within the angle
(Its interior portion. )
• Points outside the angle
(Its exterior portion. )

11. Right Angle:
An angle that forms a
square corner
Acute Angle:
An angle less
than a right angle
Obtuse Angle:
An angle greater
than a right angle

12. Two angles that have the same measure are called congruent
angles.
Congruent angles have the same size and shape.
A
B
C
300
D
E
F
300
D
E
F
300

13. Two angles that have a common vertex and a common ray
are called adjacent angles.
C
D
B
A
Common ray
Common vertex
Adjacent Angles ABD and DBC
Adjacent angles do not overlap each other.
D
E
F
A
B
C
ABC and DEF are not adjacent angles

14. Vertically opposite angles are pairs of angles formed by two
lines intersecting at a point.
APC = BPD
APB = CPD
A
DB
C
P
Four angles are formed at the point of intersection.
Point of intersection ‘P’ is the common vertex of the four
angles.
Vertically opposite angles are congruent.

15. If the sum of two angles is 900, then they are called
complimentary angles.
600
A
B
C
300
D
E
F
ABC and DEF are complimentary because
600 + 300 = 900
ABC + DEF

16. If the sum of two angles is 1800 then they are called
supplementary angles.
PQR and ABC are supplementary, because
1000 + 800 = 1800
RQ
P
A
B
C
1000
800
PQR + ABC

17. Two adjacent supplementary angles are called linear pair
of angles.
A
600 1200
PC D
600 + 1200 = 1800
APC + APD

18. A line that intersects two or more lines at different points is
called a transversal.
Line L (transversal)
BA
Line M
Line N
DC
P
Q
G
F
Line M and line N are parallel lines.
Line L intersects line
M and line N at point
P and Q.
Four angles are formed at point P and another four at point
Q by the transversal L.
Eight angles are
formed in all by
the transversal L.

19. When two parallel lines are cut by a transversal, pairs of
corresponding angles are formed.
Four pairs of corresponding angles are formed.
Corresponding pairs of angles are congruent.
GPB = PQE
GPA = PQD
BPQ = EQF
APQ = DQF
Line M
BA
Line N
D E
L
P
Q
G
F
Line L

20. Alternate angles are formed on opposite sides of the
transversal and at different intersecting points.
Line M
BA
Line N
D E
L
P
Q
G
F
Line L
BPQ = DQP
APQ = EQP
Pairs of alternate angles are congruent.
Two pairs of alternate angles are formed.

21. The angles that lie in the area between the two parallel lines
that are cut by a transversal, are called interior angles.
A pair of interior angles lie on the same side of the
transversal.
The measures of interior angles in each pair add up to 1800.
Line M
BA
Line N
D E
P
Q
G
F
Line L
600
1200
1200
600
BPQ + EQP = 1800
APQ + DQP = 1800