Hg
Name: Class 8 STICK TO WALL IN YOUR STUDY AREA
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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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Laws of exponents:
i. (x
a
)
b
= x
a*b
Power to the Power, Powers are multiplied.
ii. x
a
x
b
= x
a+b
In multiplication case, same base Powers are added.
iii. x
a
/x
b
= x
a-b
In division case, same base Powers are subtracted.
iv. x
0
= 1 Anything raised to the power zero is one.
iv. x
-m
= 1/x
m
v. x
a
y
a
= (xy)
a
vi. x
a
/y
a
= (x/y)
a
Algebraic Identities:
I. (a + b)
2
= a
2
+ b
2
+ 2ab
II. (a - b)
2
= a
2
+ b
2
- 2ab
III. (a + b)(a - b) = a
2
- b
2
Polygons:
i. Sum of all INTERIOR angles of a polygon of n sides = (n-2) * 180°
ii. Sum of all EXTERIOR angles of a polygon of n sides is always = 360°
From above, we can deduce:
iii. Sum of all INTERIOR angles of a TRIANGLE = (3-2) * 180° = 180°
iv. Sum of all INTERIOR angles of a QUADRILATERAL = (4-2) * 180° = 2 * 180° = 360°
(Since a quadrilateral is made up of two triangles, so 180° + 180° = 360° also )
v. Each INTERIOR angle of a regular polygon of n sides =
(
𝑛−2
)
∗ 180°
𝑛
vi. Each EXTERIOR angle of a regular polygon of n sides =
360°
𝑛
vii. Sum of an exterior angle and an interior angle of a polygon will be = 180°
(Since an interior angle and an exterior angle combined forms a linear pair)
viii. Number of diagonals in a polygon of n sides =
𝑛 ∗(𝑛−3)
2
Lines & Angles:
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°
