Vertical Angles
Vertical angles are a type of angle formed by two intersecting lines
Vertical angles are a type of angle formed by two intersecting lines. When two lines intersect, they create four angles in the intersection, with two of these angles being vertical angles.
Vertical angles are opposite each other and share a common vertex, but they are not adjacent angles. In other words, the lines that form the vertical angles do not have a side in common.
Properties of Vertical Angles:
1. Vertical angles are congruent: This means that the measures of the two vertical angles are equal. If one vertical angle measures x degrees, then the other vertical angle will also measure x degrees.
2. Vertical angles are always opposite each other: This implies that if you have two vertical angles, one of the angles will be opposite the other. For example, if angle A and angle B are vertical angles, then angle A will be opposite angle B.
3. Vertical angles are formed by intersecting lines: It is important to note that vertical angles are specifically formed by the intersection of two lines. If there is no intersection, there will be no vertical angles.
4. Vertical angles are not adjacent: Adjacent angles are angles that share a common side. However, vertical angles do not share a common side. They are on different pairs of opposite rays.
5. Vertical angles form a linear pair: A linear pair is a pair of adjacent angles formed when two lines intersect. While vertical angles are not adjacent, they do form a linear pair with their adjacent angles. This means that the sum of two adjacent angles would be 180 degrees.
Example:
In the diagram below, lines l and m intersect at point P, forming four angles.
A
________P________
| |
| |
C|____Q____|B
In this diagram, angle A and angle C are vertical angles, as are angle B and angle Q. Angles A and C are congruent, as are angles B and Q.
To summarize, vertical angles are a special type of angle formed by intersecting lines. They are always congruent, opposite each other, not adjacent, and form a linear pair with their adjacent angles. Understanding the properties of vertical angles can help in solving various geometrical problems and proofs.
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