In mathematics, "adjacent" generally means next to or sharing a common boundary or element. The specific meaning depends on the context.
Adjacent Angles
The most common use of "adjacent" in mathematics is in reference to adjacent angles.
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Adjacent angles are two angles that:
- Share a common vertex (corner point).
- Share a common side.
- Do not overlap.
Think of them as angles sitting side-by-side.
For example, imagine two lines intersecting. The angles formed that are next to each other are adjacent angles.
Adjacent Sides
The term "adjacent" is also used in geometry to describe the relationship between sides of a polygon, especially in triangles.
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Adjacent Sides in a Polygon: Adjacent sides are sides that share a common vertex. For example, in a square, each side is adjacent to two other sides.
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Adjacent Side in a Right Triangle (Trigonometry): In trigonometry, with respect to a specific acute angle in a right-angled triangle, the adjacent side is the side that is next to the angle (and is not the hypotenuse).
- The hypotenuse is the longest side (opposite the right angle).
- The opposite side is the side across from the angle in question.
- The adjacent side is the remaining side that forms part of the angle.
This distinction is crucial for trigonometric ratios like cosine (cos), which is defined as the ratio of the adjacent side to the hypotenuse.
Adjacent Vertices
In graph theory and geometry, "adjacent vertices" are vertices that are connected by an edge (in graph theory) or a line segment (in a polygon). They are, essentially, next to each other in the structure.
In summary, "adjacent" in mathematics describes a relationship of being next to each other or sharing a common element, the specific meaning depending on the geometrical or graphical context.
