Vertical Angles
A pair of opposite congruent angles formed by intersecting lines
Vertical angles are formed when two lines intersect at a point, creating four angles that are opposite each other. If two of the angles are adjacent, then the other two angles are also adjacent. The angle formed by the intersection of the two lines is known as the vertex angle.
Vertical angles are always congruent, meaning that they have the same angle measure. This can be proven by using the properties of angles and parallel lines. Because vertical angles are opposite each other and lie on opposite sides of the intersection point, they are not adjacent angles. Rather, they are adjacent supplementary angle pairs, meaning that their combined measures add up to 180 degrees.
For example, in the diagram below, angles 1 and 2 are vertical angles and therefore congruent. Angles 3 and 4 are also vertical angles but are not congruent because they are not opposite each other.
3 1
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2
More Answers:
Parallel Lines: Properties, Applications, And Examples In MathExploring The Angle Bisector Theorem: A Guide To Proportional Segments And Geometric Problem Solving In Triangles.
Congruent Shapes In Geometry: Definition And Properties