Adjacent Angles
Adjacent angles are a pair of angles that have a common vertex and a common side
Adjacent angles are a pair of angles that have a common vertex and a common side. In other words, they are angles that are next to each other. Adjacent angles can be formed by two intersecting lines or by a line intersecting a transversal.
When two lines intersect, they form four angles around the intersection point. Two of these angles are adjacent angles. For example, if you have two lines AB and CD intersecting at point E, the angles AEC and BEC are adjacent angles.
Similarly, when a line intersects a pair of parallel lines, it forms eight angles. In this case, adjacent angles are pairs of angles that share a common vertex and a common side between the two parallel lines. For example, if you have two parallel lines AB and CD intersected by line EF, angles AEF and BEF are adjacent angles, as well as angles CEF and DEF.
Adjacent angles are important in various ways. They can be used to find missing angle measurements or to prove geometric theorems. For example, if you know the measure of one adjacent angle, you can use it to find the measure of the other adjacent angle by using properties of angles formed by intersecting lines or by parallel lines.
In summary, adjacent angles are angles that are next to each other, sharing a common vertex and a common side. They are formed when lines intersect or when a line intersects a pair of parallel lines. Understanding adjacent angles is essential in geometry for solving problems and proving theorems.
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