The term adjacent refers to something next to each other. So adjacent angles are the angles that are next to each other. But there are certain criteria so that we can call two angles adjacent angles. As per explanation in geometry, the two angles that have a common corner point or vertex and also have a common arm are known as adjacent angles. So it can be said that any two angles generated from a single vertex and share one arm are adjacent angles. It is to be noted that adjacent angles must not overlap in any way. When three rays meet at a common point two adjacent angles are formed with the given point as the vertex.
Adjacent angles can be identified by two primary properties. The adjacent angles should be formed from a common vertex and must have an arm that is common to both angles. The adjacent angles can be complementary angles or supplementary angles to each other. If the sum of two adjacent angles is equal to 90 degrees, then they are called complementary angles and if the sum of adjacent angles is equal to 180 degrees, then they are supplementary to each other. The sum of two adjacent angles is the value of the angle formed by two non-common arms. If the sum of two adjacent angles is 90 degrees, the non-common arms are perpendicular to each other. Again, if the sum of adjacent angles is 180 degrees, then the two non-common rays form a straight line.
Properties of Adjacent Angles
Adjacent angles have some properties that help to identify them as adjacent angles. These properties are as follows:
- Adjacent angles are formed at a common vertex
- Adjacent angles have a common arm between them
- Adjacent angles do not overlap with each other
- Adjacent angles can be complementary or supplementary to each other
- Each of the adjacent angles has a common arm and a non-common arm on both sides of the common arm
Alternate Interior Angles
When two separate lines are intersected by another line, four angles are formed at the points of intersection on the inner side of two lines. The line that crosses two other lines is called a transversal. Out of the four angles formed as mentioned, the two pairs of inner angles that are formed on the opposite sides of the transversal are called alternate interior angles. So, the angles are formed on the inner side of the lines but the opposite sides of the transversal are known as the alternate interior angles. Alternate interior angles are also called ‘Z’ angles as they form a Z pattern. There is always a pair of alternate interior angles formed when two lines are intersected by another line.
Alternate interior angles are formed when the transversal intersects two lines that can be either parallel or not. When a transversal crosses two lines that are not parallel, the alternate angles formed have no geometrical relation between them. But if the lines intersected by the transversal are parallel, then the alternate angles formed are equal to each other. In other words, if the alternate interior angles have the same value, we can say that the two lines intersected by the transversal are parallel. Visit Cuemath to learn more about this topic.
Properties of Alternate Interior Angles
- Alternate angles are formed by two lines at the point of intersection with another line.
- Alternate angles are formed on the inner side of both the lines that are crossed by another line.
- Alternate angles are formed at the opposite sides of the intersecting line or transversal.
- Alternate angles are formed in pairs.
- Alternate angles have equal values when the two lines that are being intersected are parallel to each other.