Vertical Angles
A pair of opposite congruent angles formed by intersecting lines
Vertical angles are angles that are formed by two intersecting lines. These angles are opposite to each other and have equal measures. This means that if one of the angles is x degrees, then the other angle is also x degrees. The two angles are also congruent, which means that they have the same size and shape.
Vertical angles are important because they are used in many geometric proofs and calculations. For example, if two angles are known to be vertical angles, then their measures can be used to find the angles formed by other intersecting lines.
It is important to note that vertical angles are always formed by two lines intersecting at a point. If the lines are parallel or do not intersect, then vertical angles cannot be formed.
Some examples of vertical angles include:
– The angles formed by the intersection of two diagonals in a rectangle are vertical angles.
– The angles formed by the intersection of two perpendicular lines are vertical angles.
– The angles formed by the intersection of two lines that are not parallel are vertical angles.
Vertical angles are often represented using the symbol ∠, followed by the angle name or label. For example, if two angles are vertical angles and one is labeled angle 1, then the other angle would be labeled ∠2.
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