vertical angles
Vertical angles are a pair of non-adjacent angles formed by the intersection of two lines
Vertical angles are a pair of non-adjacent angles formed by the intersection of two lines. They have equal measures and are opposite each other. To understand vertical angles, let’s consider an example:
Imagine we have two intersecting lines. Label one of the lines as line AB and the other as line CD. The point of intersection between these lines is labeled as point E.
The angles formed are:
Angle AED and angle BEC: These are the vertical angles. They are opposite to each other and have equal measures.
Angle AEC and angle BED: These are known as adjacent angles. They share a common side (line AE or BE) and a common vertex (point E).
Vertical angles are always congruent. This means they have the same measure or angle value. So, if angle AED measures 50 degrees, then angle BEC will also measure 50 degrees.
Vertical angles are important in geometry because they help us prove other angles congruent. For example, if we can prove that two vertical angles are congruent, then we can also conclude that the adjacent angles formed by the intersecting lines are congruent as well.
To summarize, vertical angles are a pair of non-adjacent angles formed by the intersection of two lines. They are opposite each other, have equal measures, and are essential in proving other angles congruent.
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