Geometry, Teacher\'s Edition

• Identify similar triangles inscribed in a larger triangle.


• Evaluate the geometric mean of various objects.


• Identify the length of an altitude using the geometric mean of a separated hypotenuse.


• Identify the length of a leg using the geometric mean of a separated hypotenuse.

II.MultipleIntelligences

• One way to differentiate this lesson is to have the students teach the concepts in the lesson.


• You can do this by dividing up the content as follows.


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  1. Group 1- teaches a review of arithmetic mean.
  
  
  
  


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  2. Group 2- teaches geometric mean
  
  
  
  


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  3. Group 3- teaches finding the length of an altitude
  
  
  
  


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  4. Group 4- teaches finding the length of a leg
  
  
  
  


• If you have a large class, you can assign one group the same topic for a different perspective.


• If you choose to do this activity, DO NOT teach the content first.


• Assign students the text and let them decipher it.


• This will also give you an opportunity to observe student understanding.


• Allow time for group work and request that students use diagrams in their presentations.


• When finished, each group “teaches” their concept to the others.


• Allow time for feedback, questions and clarification.


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

III.SpecialNeeds/Modifications

• Inscribed- remind the students of the circles


• Define altitude.


• Review definition for similar objects.


• Review finding the arithmetic mean.


• Provide students with these notes to help clarify the material.


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  1. To find the length of the altitude- take the length of the segments of the divided hypotenuse and find the
     geometric mean.
  
  
  
  


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  2. To find the length of the leg- multiple line segment of divided hypotenuse times the length of the hypotenuse
     and take the square root of the product.
  
  
  
  

IV.AlternativeAssessment

• Provide feedback during presentations.


• Assess student learning during group work and presentations.

Special Right Triangles

I.SectionObjectives

• Identify and use the ratios involved with right isosceles triangles.


• Identify and use the ratios involved with 30-60-90 triangles.


• Identify and use ratios involved with equilateral triangles.


• Employ right triangle ratios when solving real- world problems.

II.MultipleIntelligences

4.8. Right Triangle Trigonometry