Adjacent
Many things can be adjacent in mathematics, such as adjacent shapes, line segments, angles, sides, etc. As in common use, the word adjacent in geometry refers to adjacent (side-by-side) elements to each other in shape. Usually applied to lines, arcs, or angles. In trigonometry, the adjacent side of a right triangle is the side following the angle.
| 1. | Meaning of Adjacent |
| 2. | Adjacent Angles |
| 3. | What is and isn't an Adjacent Angle? |
| 4. | Solved Examples |
| 5. | Practice Questions |
| 6. | FAQs on Adjacent |
Meaning of Adjacent
The meaning of adjacent is nearby or next to. An example of adjacent is two neighboring houses. We usually consider people on our street as our neighbors. Who's our next-door neighbor then? A person who lives in a house or apartment next to us. Adjacent can refer to two things, touching each other or sharing the same wall or border. What about two lines that meet at the vertex of a polygon? Can they be considered as adjacent sides? In triangles and other polygons, the two sides that meet at the vertex of the polygon are adjacent.
Adjacent Angles
In math, adjacent can be many things, but adjacent is applied mainly to line segments and angles. Any two angles that share a common ray or side, a common vertex, and whose interiors do not overlap are called adjacent angles. For example, look at the image below, the interiors of ∠ABD and ∠CBD don’t overlap, and hence they are adjacent angles.
What Is and Isn't an Adjacent Angle?
Listed below are a few important points about what can be considered as an adjacent angle and what cannot be considered as adjacent angles even though it shares the same vertex and the side.
- Adjacent angles share a vertex and a side as shown in the image below
- Angles are not considered adjacent when they only share a vertex not a side
- Angles are not considered adjacent angles when they only share a side, not a vertex
- Angles are not considered adjacent when angles a and b overlap as shown in the image below
Related Articles on Adjacent
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Practice Questions
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Example 1: Look at the hands of the clock. Do they form a pair of adjacent angles?
Solution:
In the given clock, the hour hand forms an angle with the second hand, and the second hand forms another angle with the minute hand. Both these pairs of angles lie next to each other and form a pair of adjacent angles. Therefore, the hands of the clock form adjacent angle pairs.
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Example 2: Are the angles marked as 1 and 2 in the following figures adjacent? Give reasons for your answers.
Solution
In the given figure,
Clearly, ∠1 and ∠2 have a common vertex O and a common arm OB. They have non-common arms OA and OC on both sides of the common arm OB. So, ∠1 and ∠2 are adjacent angles.
Yes, ∠1 and ∠2 are adjacent angles.
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Example 3: List 5 pairs of adjacent angles in the following figure.
Solution:
Five pairs of adjacent angles are given below.
Sr. No. Pairs of Adjacent Angles 1. ∠AOE, ∠EOC 2. ∠EOC, ∠COB 3. ∠AOC, ∠COB 4. ∠COB, ∠BOD 5. ∠EOB, ∠BOD
FAQs on Adjacent
What is the Definition of Adjacent?
Adjacent means when two things are side-by-side or next to each other. In a class, every bench has 2 students sitting next to each other is considered as adjacent. When states share a common boundary, we can refer them to as adjacent states as they are sharing the boundary and are next to each other. In math, adjacent is used to denote two sides or angles that lie next to each other, and we call them adjacent sides and adjacent angles.
What is the Definition of Adjacent Angles?
Angles are considered to be adjacent angles when two angles share a common side and vertex and do not overlap. Adjacent angles need not be equal or supplementary. There should not be any gap or overlap between two angles to be considered as adjacent angles.
What are Adjacent Sides?
Adjacent sides are sides of a polygon that have a common vertex. For example, in a triangle PQR, adjacent sides are PQ and QR as there lies a common vertex (i.e. Q) between both sides.
Are Adjacent Angles Equal?
Adjacent angles need not always be equal. Two different angles could also be considered adjacent if they satisfy all the conditions relevant for adjacent angles. In the case of a square or a rectangle, adjacent angles are equal as all the angles measure 90º.
Are Vertical Angles Non Adjacent?
No, vertical angles are always non-adjacent angles. When two lines intersect, vertical angles are formed that are not adjacent angles. These angles have a common vertex but never share a common side.
Does Adjacent mean Side by Side?
Yes, adjacent means side by side i.e as the angles are next to each other sharing the same vertex and same side. The adjacent side of a triangle is the side closest to the angle whereas the opposite side is the side across from the angle.