Vertical angles are pairs of non-adjacent angles formed when two straight lines intersect. They are located opposite each other at the point of intersection, sharing the same vertex but not a common side. When two lines cross, four angles are created, and the vertical angles are the two pairs of opposite angles among these four
. A key property of vertical angles is that they are always congruent, meaning they have equal angle measures. This is known as the Vertical Angles Theorem. For example, if two lines intersect creating angles a°, b°, c°, and d°, then the pairs (a°, c°) and (b°, d°) are vertical angles and each pair has equal measures
. The term "vertical" in vertical angles refers to the vertex where the lines intersect, not the up-down direction. Vertical angles can be any measure, including right angles (90°), if the intersecting lines are perpendicular
. In summary:
- Vertical angles are opposite angles formed by the intersection of two lines.
- They share a common vertex but no common side.
- Vertical angles are always equal in measure (congruent).
- Two pairs of vertical angles are formed at the intersection.
This concept is fundamental in geometry for solving angle-related problems involving intersecting lines
