Geometry, Teacher\'s Edition

Perpendicular Bisectors in Triangles

I.SectionObjectives

• Construct the perpendicular bisector of a line segment.


• Apply the Perpendicular Bisector Theorem to identify the point of concurrency of the perpendicular bisectors
  of the sides (the circumcenter).


• Use the Perpendicular Bisector Theorem to solve problems involving the circumcenter of triangles.

II.MultipleIntelligences

• Begin by reviewing notes on the perpendicular bisector of a line segment.


• Show how the bisector divides the line segment into two congruent segments.


• Show how it intersects the line at a right angle.


• Ask students to draw two different line segments, measure them and draw in the perpendicular bisector.


• Either walk around and check student work or do a peer check. It is important to establish understanding
  before moving on to the next section.


• Go over the Perpendicular Bisector Theorem and its converse.


• Have students use a compass and colored pencils in the next activity.


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  1. Students draw a triangle of their own design.
  
  
  
  


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  2. Students draw in the perpendicular bisectors of each line segment.
  
  
  
  


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  3. Students use a compass to draw in a circle that encompasses the triangle.
  
  
  
  


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  4. Students label the circumcenter of the diagram.
  
  
  
  


• Intelligences- linguistic, logical- mathematical, visual- spatial, bodily- kinesthetic

III.SpecialNeeds/Modifications

• Review the definitions of perpendicular and bisector.


• Write the Theorems on the board.


• Be sure that students copy those notes into their notebooks.


• Define circumcenter.


• Demonstrate how to draw in the segment bisectors and label the circumcenter.


• Review using a compass.

IV.AlternativeAssessment

• Collect and examine student drawings/diagrams to assess student understanding.


• Be sure to allow time for student questions.


• If students are having a difficult time with the in class assignments, allow them the option of working with a
  peer.


• Be sure that peer work is on task through observation and walking around.

Angle Bisectors in Triangles

I.SectionObjectives

• Construct the bisector of an angle.

4.5. Relationships Within Triangles