##### Like what you saw?

##### Create FREE Account and:

- Watch all FREE content in 21 subjects(388 videos for 23 hours)
- FREE advice on how to get better grades at school from an expert
- Attend and watch FREE live webinar on useful topics

# Point of Concurrency - Concept

###### Brian McCall

###### Brian McCall

**Univ. of Wisconsin**

J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

A **point of concurrency** is where three or more lines intersect in one place. Incredibly, the three angle bisectors, medians, perpendicular bisectors, and altitudes are concurrent in every triangle. There are four types important to the study of triangles: for angle bisectors, the incenter; for perpendicular bisectors, the orthocenter; for the altitudes, the circumcenter; for medians, the centroid.

A point of concurrency is a place where three or more, but at least three lines, rays, segments or planes intersect in one spot. If they do, then those lines are considered concurrent, or the the rays are considered concurrent. So let's look at two examples here.

If I look at this example right here we have three lines and in this spot right here we have two lines intersecting, in this spot we have two lines intersecting and here we have two lines intersecting. So none of these lines are concurrent. There is no point of concurrency.

If we look at these three lines right here, it's pretty clear to see that they all intersect in one point. So that point right there where three lines intersect would be our point of concurrency.

But why does this matter? Well, it matters in triangles when we're talking about four types of points of concurrency. The first one is formed by the three angle bisectors.

So if you're thinking about a triangle, if you're to construct a three angle bisectors, you would be constructing a special point of concurrency known as the in center, and the in center is the center of a circle that when you draw that circle it will intersect the sides exactly one time.

If you were to construct the three perpendicular bisectors of each of the three sides, then you will be finding the point of concurrency called the "circumcentre." And a circumcentre is like the in centre except for the circumcentrer circle intersects the three vertices not the three sides.

The next type is the three altitudes. So if you took your triangle and constructed your three altitudes, you'd be constructing a point of concurrency known as the "orthocenter."

The last type is a median. So if you constructed this three medians of each side connecting the vertex to the midpoint, then you'd be constructing the centroid, which is also the center of gravity or the center of mass for a given triangle.

So the reason why points of concurrency is an important vocab word is because there are four major types of points of concurrency or talking about triangles.

Please enter your name.

Are you sure you want to delete this comment?

###### Brian McCall

B.S. in Chemical Engineering, University of Wisconsin

J.D. University of Wisconsin Law School (magna cum laude)

He doesn't beat around the bush. His straightforward teaching style is effective and his subtle midwestern accent is engaging. There's never a dull moment with him.

so my teacher can't explain this in 5 weeks but I learn this in less than 3 minutes”

its hard to focus when the teacher is really really really goodlooking”

i like how it took you 3 minutes and 8 seconds to accomplish what my teacher couldn't in 3 days”

##### Concept (1)

#### Related Topics

- Constructing the Centroid 15,597 views
- Constructing a Perpendicular at a Point on a Line 11,581 views
- Duplicating a Line Segment 20,867 views
- Duplicating an Angle 14,180 views
- Constructing the Perpendicular Bisector 30,329 views
- Constructing a Perpendicular to a Line 14,304 views
- Constructing an Angle Bisector 23,369 views
- Constructing Parallel Lines 18,369 views
- Constructing Altitudes 24,438 views
- Constructing a Median 13,833 views
- Constructing a Triangle Midsegment 10,882 views
- Circumscribed and Inscribed Circles and Polygons 16,700 views
- Constructing the Incenter 10,487 views
- Constructing the Circumcenter 14,216 views
- Constructing the Orthocenter 24,457 views

## Comments (0)

Please Sign in or Sign up to add your comment.

## ·

Delete