## Vertical Angles Theorem

### The Vertical Angles Theorem states that when two lines intersect, the pairs of vertically opposite angles formed are equal

The Vertical Angles Theorem states that when two lines intersect, the pairs of vertically opposite angles formed are equal.

To understand this theorem, let’s consider a diagram. Let line AB intersect line CD at point O. The angles formed at the intersection point O, namely ∠AOB and ∠COD, are called vertically opposite angles. Similarly, ∠AOD and ∠BOC are also vertically opposite angles, as they are formed by intersecting lines.

According to the Vertical Angles Theorem, if line AB intersects line CD at point O, then ∠AOB is equal to ∠COD and ∠AOD is equal to ∠BOC. This means that the measure of the vertically opposite angles is the same.

This theorem can be proven using angle relationships and the fact that the measures of angles around a point add up to 360 degrees. By examining the angles involved in the intersecting lines, we can conclude that the vertically opposite angles are congruent or equal.

For example, if ∠AOB = 60 degrees, then ∠COD will also be 60 degrees, and ∠AOD and ∠BOC will also be 120 degrees. This holds true for any measures of angles formed by intersecting lines.

The Vertical Angles Theorem is an important concept in geometry as it helps us determine the relationships between angles formed by intersecting lines. It allows us to solve problems involving angles, parallel lines, and transversals. It is also used as a basis for proving other theorems related to angles.

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