Vertical Angles Theorem
The Vertical Angles Theorem states that when two lines intersect, the pairs of opposite angles formed are equal
The Vertical Angles Theorem states that when two lines intersect, the pairs of opposite angles formed are equal. These opposite angles, known as vertical angles, are congruent and have the same measure.
To better understand the theorem, let’s consider the following diagram:
A
|
| x °
——————- Line AB
|
|
B
In the diagram above, two lines intersect at point B, forming four angles: Angle ABO, Angle OBA, Angle ABO, and Angle OBA.
According to the Vertical Angles Theorem, Angle ABO is congruent to Angle OBA, and Angle AOB is congruent to Angle BOA.
This theorem is based on the idea that when two lines intersect, they create pairs of opposite angles that have equal measures. Opposite angles share the same vertex but are on different rays and lie on opposite sides of the intersection.
The Vertical Angles Theorem is an important concept in geometry and is used to prove various properties and theorems involving angles, lines, and transversals.
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