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. These angles share a common vertex but have different rays. In other words, vertical angles are opposite angles formed by two intersecting lines.
Properties of Vertical Angles:
1. Vertical angles are congruent: This means that the measures of vertical angles are always equal. If one angle measures x degrees, then the other vertical angle formed will also measure x degrees.
2. Vertical angles are formed by two pairs of opposite rays: When two lines intersect, they form two pairs of vertical angles. The pairs of vertical angles are located opposite each other.
3. Vertical angles are not adjacent: Adjacent angles are angles that share a common ray or side. However, vertical angles do not share a common ray or side, but instead, they are formed by opposite rays.
4. Vertical angles form a linear pair with adjacent angles: When two adjacent angles and their non-common sides form a straight line, they are called a linear pair. Vertical angles are always part of a linear pair with two adjacent angles.
5. Vertical angles are the same size: Since vertical angles are congruent (or equal in measure), they have the same angle size. This property holds true for any pair of vertical angles.
Understanding and recognizing vertical angles is crucial in various mathematical applications, including geometry, proofs, and theorems. They often play a significant role in solving geometric problems involving angles and lines.
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