Question

Prove that if two lines intersect each other then the vertically opposite angles are equal.

Answer 1

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

What is a line?

A line is a one-dimensional figure, which has length but no width. A line is made of a set of points which is extended in opposite directions infinitely.

To prove, two lines intersect each other then the vertically opposite angles are equal.

Suppose there are two lines AB and CD intersecting at a point O.

So, the angles a and c ; b and d are vertically opposite.

Now taking line AB,

Since sum of angles made on a straight line is 180°.

Thus ∠a + ∠b = 180°    ...(i)

Similarly taking line CD,

∠b + ∠c = 180°            ....(ii)

Comparing eq (i)  and (ii) we get,

∠a + ∠b = ∠b + ∠c

Therefore, we get

∠a = ∠c

which are vertically opposite angles.

Taking line CD,

Since sum of angles made on a straight line is 180°.

Thus ∠c + ∠b = 180°    ...(iii)

Similarly taking line CD,

∠c + ∠d = 180°            ....(iv)

Comparing eq (iii)  and (iv) we get,

∠c + ∠b = ∠c + ∠d

Therefore, we get

∠b = ∠d

which are vertically opposite angles.

Thus, if two lines intersect each other then the vertically opposite angles are equal.

To learn more about angles:

brainly.com/question/11337367

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