Special Segments in a Triangle

Jill Casey, Oct 18, 2017

Table of Contents

  1. Learn about special segments and points of concurrency in a triangle.
    1. Perpendicular Bisectors
    2. Angle Bisectors
    3. Medians
    4. Altitudes
  2. Practice recognizing points of concurrency
    1. Practice Problem #1
    2. Practice Problem #2
    3. Practice Problem #3
    4. Practice Problem #4
  3. Practice recognizing special segments in a triangle
    1. Practice Problem 1
    2. Practice Problem 2
    3. Practice Problem 3

1.

Learn about special segments and points of concurrency in a triangle.

Construct and discover the points of concurrency of a triangle.

  • 1. Perpendicular Bisectors
  • 2. Angle Bisectors
  • 3. Medians
  • 4. Altitudes

1.1.

Perpendicular Bisectors

You will be constructing 3 perpendicular bisectors in one triangle.
Directions:
1. Select the triangle tool and create an acute, scalene triangle. Make sure to select the pointer tool afterwards in order to not keep creating polygons![br]2. Select the point and line tool (4th from the left) and choose perpendicular bisector from the drop down menu. The directions on how to select the items in order to create a perpendicular bisector will appear at the bottom of the screen. (Select one segment.)[br]3. You will do this two more times to create three perpendicular bisectors.
What do you notice about the three perpendicular bisectors?
This point is special! You will discover why.[br]Step 1: Choose the circle tool and circle with center through a point. [br]Step 2: Click on the intersection of the perpendicular bisectors to make that point the center of a circle.[br]Step 3: Drag the circle until you can click on one of the angles of the triangle.
What do you notice about this circle?
– Jill Casey

1.2.

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1.3.

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1.4.

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2.

Practice recognizing points of concurrency

Let's see if you remember what you just learned!

  • 1. Practice Problem #1
  • 2. Practice Problem #2
  • 3. Practice Problem #3
  • 4. Practice Problem #4

2.1.

Practice Problem #1

What is the name of the point of concurrency for point D?
– Jill Casey

2.2.

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2.3.

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2.4.

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3.

Practice recognizing special segments in a triangle

Let's see if you recognize medians, altitudes, perpendicular bisectors and angle bisectors.

  • 1. Practice Problem 1
  • 2. Practice Problem 2
  • 3. Practice Problem 3

3.1.

Practice Problem 1

Segment CL is a(n):
– Jill Casey

3.2.

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3.3.

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