Mathematics

# Two lines intersecting each other, prove that vertically opposite angles are equal.

##### SOLUTION
If two lines i.e. AB & CD intersect each other. They have two pair of opp. angles.

i.e.
$\angle AOC , \angle DOB, \angle AOB, \angle COB.$

To prove :- $\angle AOC = \angle DOB$ & $\angle AOD = \angle COB$

Proof :-
$\angle AOC + \angle AOD = 180^{\circ}$  [linear pair] ___(1)

$\angle AOD + \angle BOD = 180^{\circ}$   [linear pair] ___(2)

from eq. (1) & (2)

$\angle AOC + \angle AOD = \angle AOD + \angle BOD$

i.e.  $[\angle AOC = \angle BOD]$

Similarly $[\angle AOD = \angle COB]$ Hence proved.

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Subjective Medium Published on 09th 09, 2020
Questions 120418
Subjects 10
Chapters 88
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