Question

Please answer the question fast.
Class 9th.
Correct answer - BRAINLIEST
Incorrect answer - REPORTED.
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PLZ ANSWER FAST​

Answer 1

(i) V.O.A

- Vertically Opposite angles

From figure 1

we have two intersecting lines.

we get ∠a, ∠b, ∠c, ∠d

Here,

∠b = ∠d

They are Vertically opposite angles

and

other vertically opposite angles are

∠a = ∠c

$\rule{200}2$

(ii) A.I.A

- Alternate Interior Angles

See in figure 2

Here E and F are two parallel lines, n is intersecting line

So,

∠x = ∠x`  A.I.A

And

∠y = ∠y` A.I.A

$\rule{200}2$

(iii) Corresponding Angles

In figure 3

the corresponding angles are -

∠a = ∠e

∠d = ∠h

∠b = ∠f

∠c = ∠g

Answer 2

Vertically Opposite Angle :-

The angles which are vertically opposite to each other are known as vertically opposite angle.

Theorems :- ( In fig. 1 )

$\angle \sf{AOD} = \angle \sf{COB}\\ \angle \sf{AOC} = \angle \sf{DOB}$

They are equal because vertically opposite angles are always equal.

$\rule{200}2$

Alternate Interior Angle :-

Two non - adjacent lines made by crossing of two lines by a third lines.

Theorem :- ( In fig. 2 )

$\angle \sf{3} = \angle \sf{6} \\ \angle \sf{4 } = \angle \sf{5}$

$\rule{200}2$

Corresponding angles and Its Converse :-

When two parallel lines are cut by a transverse the resulting corresponding angles are congruent.

Theorem :- ( In fig. 3 )

$\angle \sf{2} = \angle \sf{1}$

$\rule{200}2$