Hg
Name: Class 9
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___________________________________________________________________________________________________________________________________
The Hg Classes (8
th
to 12
th
) By: Er Hershit Goyal (B.Tech. IIT BHU), 134-SF, Woodstock Floors, Nirvana Country, Sector 50, GURUGRAM +91 9599697178.
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Lines and Angles
Lines:
• A line is an indefinite length, denoted by
.
• A part of a line with two end points is called a line segment, denoted by
.
• A part of a line with one end point is called a ray, denoted by
.
• If 3 or more points, lie on the same line, they are called collinear points, otherwise they are non-
collinear.
Angles:
• An angle is formed when two rays originate from the same end-point. The rays making the angle are
called arms and the end point is called vertex.
• Types of angles:
o Acute > 0
o
but < 90
o
o Right = 90
o
o Obtuse > 90
o
but < 180
o
o Straight = 180
o
o Reflex > 180
o
but < 360
o
o Complete = 360
o
• Complementary angles – whose sum is 90
o
o If an angle is x
o
, then its complement is (90 – x)
o
and vice versa.
• Supplementary angles – whose sum is 180
o
o If an angle is x
o
, then its complement is (180 – x)
o
and vice versa.
• Linear Pair - Angles on a straight line form a linear pair. In the figure
on the right, ABD & CBD form a linear pair, their sum is 180
o
.
• Vertically Opposite Angles – When two lines intersect two pairs of vertically opposite angles are
formed.
In the fig, AOC = DOB and
AOD = BOC
• Angles formed when two parallel lines are intersected by a transversal:
Vertically Opposite Angles
a = d & b = c
e = h & f = g
Corresponding Angles
a = e & b = f
h = d & g = c
Linear Pair
a + b = 180° e + f = 180°
b + d = 180° f + h = 180°
d + c = 180° h + g = 180°
c + a = 180° g + e = 180°
Alternate Interior Angles
d = e & c = f
Co-interior angles
c + e = 180° & d + f = 180°
Angles in a circle
a + b + c + d = 360°
e + f + g + h = 360°
Alternate Exterior Angles
a = h & b = g
Co-exterior angles
b + h = 180° & a + g = 180°
