Geometry, Teacher\'s Edition

• Show a diagram on the board that introduces the students to the Concurrency of Medians Theorem.


• Use the diagram to show each median being drawn in then show the point of intersection, the centroid.


• Introduce the vocabulary word as the material is covered.


• You may want to allow time for the students to try this with a triangle of their own creation.


• This will give them a good understanding of the concepts.


• Then complete the second part of the lesson.


• Pg. 300 -Complete the activity in Example 2 together as a class.


• Ask the students to write down the answers to the two questions.


• Then open up the discussion to a brainstorming session.


• Write student responses on the board.

III.SpecialNeeds/Modifications

• Write all definitions on the board/overhead.


• Define median of a triangle.


• Define concurrent


• Define centroid and show the connection between concurrent and centroid.


• Review the midpoint formula.


• Review the distance formula.


• Review using the Geometer’s Sketchpad.


• Define Napolean’s Theorem.

IV.AlternativeAssessment

• Assessment is completed through observation and discussion.

Altitudes in Triangles

I.SectionObjectives

• Construct the altitude of a triangle.


• Apply the Concurrency of Altitudes Theorem to identify the point of concurrency of the altitudes of the
  triangle (the orthocenter).


• Use the Concurrency of Altitudes Theorem to solve problems involving the orthocenter of triangles.

II.MultipleIntelligences

• Begin this lesson with a real life example about altitude. You could use a plane and review the meaning of the
  word altitude with the students. This will help them to draw associations as they work with the concept.


• Define altitude.


• Use these steps to find the altitude of a triangle.


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  1. Identify the vertex you are using.
  
  
  
  


• 
  
  
  
  2. Find the side of the triangle opposite the vertex or where this side should be located.
  
  
  
  


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  3. Draw a straight line from the vertex to that opposite side, draw the side in if it does not exist in the original
     triangle.
  
  
  
  


• Show the two examples with the acute triangle and the obtuse triangle. Have students draw these two examples
  in their notebooks.


• Define the Concurrency of Triangles Altitude Theorem


• Define orthocenter

4.5. Relationships Within Triangles