Point Of Concurrency Of Triangle

Understanding the Points of Concurrency in a Triangle

What are the points of concurrency in a triangle and what is mathematically special near each of them?

The centroid is the betoken of concurrency (intersection) of the iii medians of a triangle. A median is a segment joining a vertex of a triangle with the midpoint of the reverse side.

The centroid of triangle ABC is point D.

An orthocenter is the point of concurrency of the three altitudes of a triangle. An altitude is the perpendicular line fatigued from a vertex to the opposite side.

The orthocenter of triangle ABC is point O.

An incenter is the point of concurrency of the three angle bisectors of a triangle. An angle bisector is the ray which bisects an angle, or divides the angle into two coinciding angles.

The incenter of triangle ABC is point I.

A circumcenter is the signal of concurrency of the three perpendicular bisectors of a triangle. A perpendicular bisector is a segment which bisects a segment and forms right angles.

The circumcenter of triangle ABC is indicate Thousand.

To see how these points of concurrency are synthetic, delight sentry my brusque Screencast video.

Now that you have seen how to construct a triangle's points of concurrency using geometry, how could you use coordinate geometry and algebra to identify the points of concurrency?

Given points A(10,7) B(ten,1) and C(two,1), find the coordinates of the following:

centroid
orthocenter
incenter
circumcenter

Check your answers using this handy Point of Concurrency web calculator.

About Ms. Miles

I've taught mathematics for over 22 years. I love education math. Interests outside of teaching include learning and doing math, playing the piano, singing in a worship squad, origami, kayaking, bicycling, swimming, collecting sea glass and shells.

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