Points of Concurrency

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Points of Concurrency

• What did you learn??

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Acute Triangle

• Point of Concurrency
• Circumcenter
• Centroid
• Incenter
• Orthocenter

• Location
• Inside
• Inside
• Inside
• Inside

3
Obtuse Triangle

• Poinnt of Concurrency
• Circumcenter
• Centroid
• Incenter
• Orthocenter

• Location
• Outside
• Inside
• Inside
• Outside

4
Right Triangle

• Point of Concurrency
• Circumcenter
• Centroid
• Incenter
• Orthocenter

• Location
• Midpoint of Hypotenuse
• Inside
• Inside
• Vertex of the right angle

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Equilateral Triangle

• Point of Concurrency
• Circumcenter
• Centroid
• Incenter
• Orthocenter

• Location
• Inside
• Inside
• Inside
• Inside

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Answer these questions

• The point equally distant from the three sides of
  a triangle is?
• The center of gravity of a triangle?
• The point equidistant from the three vertices is?
• A point that is sometimes outside of a traingle?
• A point that is on the hypotenuse of a right
  triangle?

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Theres more

• A point that is at the vertex of a right
  triangle?
• For what type of triangle are all 4 points of
  concurrency the same point?
• This one is a guessWhen all 4 points of
  concurrency are collinear, what type of triangle
  do you have?

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Take another guess

• Has anyone ever heard of Euler?
• What is the Euler Line?
• Which three points of concurrency are always on
  the Euler Line?

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a)Find the coordinates of the midpoints L,M, and
N b) Find the equations of MA, BN, and CL
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• c) Find the coordinates of P, the intersection of
  AM and BN
• d) Is P on CL?
• e) Use the distance formula to show that point P
  is 2/3 of the distance from each vertex to the
  midpoint of the opposite side.

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There is a shortcut for finding the centroid of a
triangle. Average the x coordinates and average
the y coordinates.