Angle Pair Relationships

 Introduction

A definition of an angle would be that an angle is the union of two rays that have the same endpoint. The sides of the angles are the two rays, while the vertex is their common endpoint. stands for an angle. You can put it in front of three letters which represent points. The first and third letters represent points on each of the rays that form one of the sides. The middle letter represents the vertex. As you can see in the diagram, each point is represented in the written form. The letters can go either way - that is, first and last letter are interchangeable. So, that angle could either be ABC or CBA. Since B is the vertex, it is always in the middle of the two letters. You can also name an angle by just the letter of its vertex. So, for the example in the picture, the angle could also be labeled B. That's only if there are no other angles that share the same vertex. There is a third way to label angles.

Pairs of angles

In geometry, pairs of angles can relate to each other in several ways. Some examples are complementary angles, supplementary angles, vertical angles, alternate interior angles, alternate exterior angles and corresponding angles.

Two angles are called complementary angles if the sum of their degree measurements equals 90 degrees. One of the complementary angles is said to be the complement of the other.

Two angles are called supplementary angles if the sum of their degree measurements equals 180 degrees. One of the supplementary angles is said to be the supplement of the other.

Two pairs of angles are formed by two intersecting lines. Vertical angles are opposite angles in such an intersection. Vertical angles are equal to each other.

When a line intersects a pair of parallel lines alternate interior angles are formed. Alternate interior angles are equal to each other.

One way to remember alternate exterior angles is that they are the vertical angles of the alternate interior angles. Alternate exterior angles are equal to one another.

When a line intersects a pair of parallel lines corresponding angles are formed. corresponding angles are equal to each other.

Formation of angle pairs

When two parallel lines is cut by a transversal eight angles are formed. Among these all the acute angles are congruent. All the obtuse angles are congruent. The two different angle measurements are supplementary.

• Among these corresponding angles are congruent.
• Alternate interior and alternate exterior angles are congruent.
• Also same side interior angles and same side exterior angles are supplementary.
• Vertical angles are congruent.
• Adjacent angles are supplementary.
• Adjacent angles form straight lines.
• Since the sum of the measures of a linear pair of angles is 180, we can say that two angles that form a linear pair is supplementary.