Lesson Plan
Class-9th
Topic:- Lines and Angles
Ray:- Part of a line with one end point is called ray.
A
B
Angle:- (i) Angle is a measure of rotation of a given ray
about its initial points.
A
O
B
(ii) An angle is formed when two rays originate from the
same end point. The rays making an angle are called
the arms of the angle and the end point is called the
vertex of the angle.
Types of Angles:(i) Acute angle:- Measure of an angle greater than 00 but less than 900 .
(ii) Obtuse angle:- Measure of an angle greater than 900 but less than
1800 .
(iii) Right angle:- Measure of an angle is exactly 900.
(iv) Straight angle:- Measure of an angle exactly 1800.
(v) Reflex angle:- Measure of an angle greater than 1800 but less than
3600.
(vi) Complete angle:- Measure of an angle exactly 3600 or measure of
an angle in one revolution.
Pair of angles:(i) Complementary angles:- Two angles whose sum is 900.
(ii) Supplementary angles:- Two angles whose sum is 1800.
(iii) Adjacent angles:- Two angles are called adjacent angles, if:
(a) they have the same vertex,
(b) they have a common arm,
(c) uncommon arms are on either side of the common arm.
(iv) Linear pair angles:- Two adjacent angles are said to form a linear
pair of angles. If their uncommon arms are two opposite rays.
The sum of linear pair angles is 1800.
(v) Vertically opposite angles:A
D
x
z
B
C
Theorem:- if two lines intersect each other, then the vertically opposite
angles are equal.
Given:- Pair of vertically opposite angles: (i) x and z (ii) y and w
To prove:- (i) x = z
(ii) y = w
Proof:- x +y = 1800 and y + z = 1800 (by the defn of linear pair
angles).
From both the equation we have,
x + y = y +z ( since two things which are equal to same things
are equal to each other).
Or
x = z …………..result (i)
Again
y + z = 1800 and z + w = 1800 ( by the defn of linear pair
angles).
From both the equation we have,
y + z = z + w ( since two things which are equal to same
things are equal to each other).
Or
y = w…………..result (2).
Example: Lines AB and CD intersect at O. if ∠𝐴𝑂𝐶 + ∠𝐵𝑂𝐸 = 700 and
∠𝐵𝑂𝐷 = 400, find ∠𝐵𝑂𝐸 and reflex ∠𝐶𝑂𝐸.
C
E
A
B
D