Question

If two lines intersect each other then the pairs of Vertically opposite angles thus formed are equal. Prove this statement

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Given,

Two lines intersect each other.

To prove,

The pair of vertically opposite angles are equal.

Solution,

Here, we are given that two lines are intersecting each other.

Refer to the figure.

The angles formed at the intersection of the 2 lines are:

∠1, ∠2, ∠3, and ∠4.

It can be seen that here,

∠1, ∠3, and, ∠2, ∠4 are the pairs of vertically opposite angles.

We need to prove ∠1 = ∠3, and, ∠2 = ∠4.

So firstly, it can be seen that ∠1 and ∠2 form a linear pair.

⇒ ∠1 + ∠2 = 180°     ...(1)

Also, ∠2 and ∠3 again form a linear pair.

⇒ ∠2 + ∠3 = 180°     ...(2)

From equations (1) and (2),

∠1 + ∠2 = ∠2 + ∠3

⇒ ∠1 = ∠3

So, ∠1 and ∠3, which are vertically opposite angles, are proved equal.

Similarly, it can also be proved that

∠2 = ∠4.

So, the pairs of vertically opposite angles which are, ∠1 and ∠3, and, ∠2 and ∠4, are equal.

Hence, it is proved that if two lines intersect each other, then the pairs of vertically opposite angles thus formed are equal.