Concurrent Lines

Concurrent lines are the lines, in 2-D geometry, which intersect each other exactly at one point. The meaning of concurrent is happening at the same time or point. That means, when two or more lines pass through a single point, they are concurrent to each other. And the point which is common to all those lines is called the point of concurrency. This property of concurrency can also be seen in the case of triangles.

In the figure given below, you can see the lines colored in orange, black and purple, are all crossing the point O. Hence, all these three lines are concurrent with each other.

Concurrent Lines

Concurrent Line Segments and Rays

When three or more line segments, intersect each other at a single point, then they are said to be concurrent line segments. See the figure below, where AB, CD and EF are three line segments and are intersecting each other at one point O. Hence, we can apply the concurrency to line segments also.

Concurrent Line-Segment

When three or more Rays in 2-D plane cuts or meets at a single point, then they are called Concurrent Rays. The single point is the point of concurrency for all the rays. Given, in the below figure, three rays PQ, RS and MN, which are intersecting at a point O, are concurrent to each other.

Concurrent Rays

Difference Between Concurrent Lines and Intersecting Lines

As we have already understood, if any three lines or line segments or rays are having a single intersection point, they are said to be in concurrency. While, in the case of intersecting lines, there are only two lines or line segments or rays that intersect with each other. We can write the difference in a tabular form.

Concurrent Lines

Intersecting LInes

Three or more lines pass through a single point.

Only two lines intersect each other

The single point is called a point of concurrency.

The point where two lines intersect is called the point of intersection.

Example:

Example of concurrent lines

Example:

Intersecting lines

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