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What room the clues of concurrency in a triangle and also what is mathematically special around each the them?

The centroid is the point of concurrency (intersection) the the 3 medians the a triangle. A median is a segment joining a vertex of a triangle through the midpoint of opposing side.

You are watching: Point of concurrency in a triangle

" data-medium-file="https://aufdercouch.net.files.aufdercouch.net.com/2012/04/picture-13.png?w=300" data-large-file="https://aufdercouch.net.files.aufdercouch.net.com/2012/04/picture-13.png?w=301" class="size-full wp-image-1131" title="Picture 1" alt="" src="https://aufdercouch.net.files.aufdercouch.net.com/2012/04/picture-13.png?w=640" srcset="https://aufdercouch.net.files.aufdercouch.net.com/2012/04/picture-13.png 301w, https://aufdercouch.net.files.aufdercouch.net.com/2012/04/picture-13.png?w=150 150w" sizes="(max-width: 301px) 100vw, 301px" />The centroid of triangle abc is point D.

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

" data-medium-file="https://aufdercouch.net.files.aufdercouch.net.com/2012/04/picture-21.png?w=292" data-large-file="https://aufdercouch.net.files.aufdercouch.net.com/2012/04/picture-21.png?w=292" class="size-full wp-image-1132" title="Picture 2" alt="" src="https://aufdercouch.net.files.aufdercouch.net.com/2012/04/picture-21.png?w=640" srcset="https://aufdercouch.net.files.aufdercouch.net.com/2012/04/picture-21.png 292w, https://aufdercouch.net.files.aufdercouch.net.com/2012/04/picture-21.png?w=150 150w" sizes="(max-width: 292px) 100vw, 292px" />The orthocenter that triangle abc is point O.

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

" data-medium-file="https://aufdercouch.net.files.aufdercouch.net.com/2012/04/picture-31.png?w=300" data-large-file="https://aufdercouch.net.files.aufdercouch.net.com/2012/04/picture-31.png?w=330" class="size-full wp-image-1134" title="Picture 3" alt="" src="https://aufdercouch.net.files.aufdercouch.net.com/2012/04/picture-31.png?w=640" srcset="https://aufdercouch.net.files.aufdercouch.net.com/2012/04/picture-31.png 330w, https://aufdercouch.net.files.aufdercouch.net.com/2012/04/picture-31.png?w=150 150w, https://aufdercouch.net.files.aufdercouch.net.com/2012/04/picture-31.png?w=300 300w" sizes="(max-width: 330px) 100vw, 330px" />The incenter that triangle alphabet is point I.

A circumcenter is the point of concurrency of the 3 perpendicular bisectors that a triangle. A perpendicular bisector is a segment i m sorry bisects a segment and forms appropriate angles.

" data-medium-file="https://aufdercouch.net.files.aufdercouch.net.com/2012/04/picture-41.png?w=300" data-large-file="https://aufdercouch.net.files.aufdercouch.net.com/2012/04/picture-41.png?w=329" class="size-full wp-image-1135" title="Picture 4" alt="" src="https://aufdercouch.net.files.aufdercouch.net.com/2012/04/picture-41.png?w=640" srcset="https://aufdercouch.net.files.aufdercouch.net.com/2012/04/picture-41.png 329w, https://aufdercouch.net.files.aufdercouch.net.com/2012/04/picture-41.png?w=150 150w, https://aufdercouch.net.files.aufdercouch.net.com/2012/04/picture-41.png?w=300 300w" sizes="(max-width: 329px) 100vw, 329px" />The circumcenter that triangle alphabet is suggest M.

To see exactly how these point out of concurrency space constructed, please watch my short Screencast video.

Now that you have seen exactly how to build a triangle’s points of concurrency using geometry, how might you usage coordinate geometry and algebra to recognize the points of concurrency?

Given points A(10,7) B(10,1) and C(2,1), find the collaborates of the following:



Check your answers utilizing this handy allude of Concurrency web calculator.

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About Ms. Miles

I"ve taught mathematics for over 22 years. I love teaching math. Interests outside of teaching include learning and doing math, play the piano, singing in a prayer team, origami, kayaking, bicycling, swimming, collecting sea glass and also shells.




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