Points of Concurrency

Paul Jorgens, May 9, 2017

Table of Contents

  1. The Centroid
    1. Construct a Midpoint
    2. Construct Medians
    3. Centroid
  2. The Circumcenter
    1. Perpendicular Bisector
    2. Bisecting the sides of a triangle
    3. Circumcenter
  3. The Orthocenter
    1. Perpendicular Lines
    2. Altitudes
    3. Orthocenter
  4. The Incenter
    1. Bisect an Angle
    2. Angle Bisectors
    3. The Incenter
  5. Euler's Line
    1. Points of Concurrency of a Triangle
    2. Euler's Line

1.

The Centroid

  • 1. Construct a Midpoint
  • 2. Construct Medians
  • 3. Centroid

1.1.

Construct a Midpoint

Use the tools to find the midpoint of the line segment.
Describe your method for finding the midpoint.
– Paul Jorgens

1.2.

–

1.3.

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2.

The Circumcenter

  • 1. Perpendicular Bisector
  • 2. Bisecting the sides of a triangle
  • 3. Circumcenter

2.1.

Perpendicular Bisector

Construct a perpendicular bisector
Describe your steps for constructing the perpendicular bisector.
– Paul Jorgens

2.2.

–

2.3.

–

3.

The Orthocenter

  • 1. Perpendicular Lines
  • 2. Altitudes
  • 3. Orthocenter

3.1.

Perpendicular Lines

Construct a line through point C perpendicular to line AB.
Describe how you constructed the perpendicular line.
– Paul Jorgens

3.2.

–

3.3.

–

4.

The Incenter

  • 1. Bisect an Angle
  • 2. Angle Bisectors
  • 3. The Incenter

4.1.

Bisect an Angle

Bisect Angle A
Describe your method for bisecting an angle.
– Paul Jorgens

4.2.

–

4.3.

–

5.

Euler's Line

  • 1. Points of Concurrency of a Triangle
  • 2. Euler's Line

5.1.

Points of Concurrency of a Triangle

The four points of concurrency are constructed in the triangle.[br]
Can you get all four points in the same position? Describe the triangle.
– Paul Jorgens

5.2.

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