Question

If two lines interest each other, then vertically opposite angles are________
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Answer 1

Answer:

Step-by-step explanation:

EQUAL

Answer 2

If two lines intersect each other , then vertically opposite angles are equal .

Vertically opposite angles in a short way are called as VOA .

How do we prove that Vertically Opposite Angles are equal ?

(Refer to the attachment along )

Step 1 : If we consider only the right side of the intersecting lines ; we see that they are forming a linear pair of 2 angles namely ∠AOB and ∠AOC . We know that when we add two adjacent angles while forming a linear pair their sum is 180°

Step 2 : We can write the above statement in symbolic form as : ∠AOB + ∠AOC = 180°

Step 3 : On the other side ; we can observe the same thing that ; two linear pairs are formed and this in symbolic form can be written as : ∠AOD + ∠COD = 180°

Step 4 : When we consider both the forms :

∠AOB + ∠AOC = ∠AOD + ∠COD

∠AOB = ∠COD

(VOA)