Math 402 Section M13

Assignment 4

Due Thursday September 20

Unless otherwise stated, all problems are from the text
Geometry with Geometry Explorer by Michael Hvidsten (McGraw Hill, 2005)

  1. 2.6.2, 2.6.4, 2.6.12
  2. Do the following construction and answer the questions

 

Construction:

  1. Using Geometry Explorer draw a triangle and mark the following 6 points:
    1. The midpoints of the three sides (label these M1, M2, M3)
    2. The feet of the three altitudes (label these A1, A2, A3)
  2. Find the orthocenter and then mark the following 3 points:
    1. The midpoints of the segments joining the vertices to the orthocenter  (label these m1, m2, m3).
  3. Pick any three of the nine points constructed in (1a, 1b, 2a) and draw the circle defined by the three points.

 

Assignment:

  1. Describe what you notice about the circle you drew. Explain why the circle is called the nine-point circle.
  2. Show that the triangle with vertices m1, m2, m3 is similar to the triangle you started with and that the corresponding pairs of sides are parallel.
  3. Print a copy of your construction (you can find Print in the File menu) and include it with your homework.

 

Definitions

1. An altitude of a triangle is a perpendicular dropped from a vertex to the opposite side, i.e. it is the line passing through the vertex and perpendicular to the opposite side.

2. The orthocenter of a triangle is the point of intersection of the three altitudes.

 

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Last modified September 14, 2007