Points of Concurrency

Paul Jorgens, alyssa, Sep 25, 2018

Table of Contents

  1. The Circumcenter
    1. Bisecting the sides of a triangle
    2. Circumcenter
  2. The Incenter
    1. Angle Bisectors
    2. The Incenter
  3. The Centroid
    1. Construct Medians
    2. Centroid
  4. The Orthocenter
    1. Altitudes
    2. Orthocenter

1.

The Circumcenter

  • 1. Bisecting the sides of a triangle
  • 2. Circumcenter

1.1.

Bisecting the sides of a triangle

Construct the perpendicular bisectors. I have added the perpendicular bisector tool.
Drag a corner of the triangle. The intersection of the three perpendicular bisectors is called the circumcenter.Is it possible for the circumcenter to be outside the triangle? If so, describe the triangle.
Is it possible for the circumcenter to be on a side of the triangle? If so, describe the triangle and the position of the circumcenter.
– Paul Jorgens

1.2.

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2.

The Incenter

  • 1. Angle Bisectors
  • 2. The Incenter

2.1.

Angle Bisectors

You constructed an angle bisector. I added the angle bisector tool. Use the tools to find the angle bisectors of the triangle.
Drag a vertex of the triangle. What do you notice about the intersection of the angle bisectors?
– Paul Jorgens

2.2.

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3.

The Centroid

  • 1. Construct Medians
  • 2. Centroid

3.1.

Construct Medians

I gave you a midpoint tool. Use it to find the medians of the triangle.
Drag the vertices of the triangle to change its shape.[br][br]What do you notice about the medians?
– Paul Jorgens

3.2.

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4.

The Orthocenter

  • 1. Altitudes
  • 2. Orthocenter

4.1.

Altitudes

You constructed a perpendicular line. I added the perpendicular line tool. Use the tools to find the altitudes of the triangle.
Drag a corner of the triangle.The point of intersection is called the orthocenter.Is it possible for the orthocenter to be outside the triangle? If so, describe the triangle.
Is it possible for the orthocenter to be on the triangle? If so, describe the triangle and the position of the orthocenter.
– Paul Jorgens

4.2.

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