# Corresponding Angles

## Definition

When a line known as intersecting traversal crosses a pair of straight lines, corresponding angles are formed. Corresponding angles are the pair of angles formed on a different intersection in the same relative position.

To understand corresponding angles some important terms must be understood.

## Angle

The angle is defined as the distance between two lines (called rays) that meet at a single point (known as the vertex). 90° right angles are probably familiar to you. All angles are measured in degrees.

## Intersection

An intersecting line is formed by two or more lines crossing one another and forming multiple angles at the vertex. Whenever two lines touch or cross, they are said to be intersecting.

## Parallel lines

A parallel line is unique in that it cannot touch or intersect with any other line, regardless of how long it extends for. They always remain the same distance apart. Corresponding angles can be used to check whether two lines are parallel.

Transversal

An intersection or crossing of parallel lines is called a transversal.

Types of Corresponding angles

There are two types of corresponding angles.

• Corresponding angles formed by parallel lines and transversals
• Corresponding angles formed by non-parallel lines and transversals

Corresponding angles Explanation

When two parallel lines a and b are intersected by a transversal.

The following corresponding angles are formed.

[katex]\angle1\;and\;\angle5-above\;the\;line\;left\;of\;transversal [/katex].

[katex]\angle3\;and\;\angle7-below\;the\;line\;left\;of\;transversal [/katex].

[katex]\angle2\;and\;\angle6-above\;the\;line\;right\;of\;transversal[/katex].

[katex]\angle4\;and\;\angle8-below\;the\;line\;right\;of\;transversal[/katex].

## Important postulate about Corresponding Angles

When lines are parallel

An angle is congruent or has the same measure when two parallel lines are cut by a transversal.

[katex]\angle1\;and\;\angle5[/katex]. have the same measure and are corresponding angles.

When lines are not-parallel

When two not-parallel lines are intersected by a transversal the corresponding angles formed are not congruent.

[katex]\angle(a)\;and\;\angle(e)[/katex]are corresponding but not congurrent.