Geometry, Teacher\'s Edition

IV.AlternativeAssessment

• Review student thinking by observing their work during the observations.


• Are the students able to come to conclusions about each theorem before it is actually taught?


• Is there higher level thinking involved?


• Can the students verbalize the steps to working through an example?

Common Tangents and Tangent Circles

I.SectionObjectives

• Solve problems involving common internal tangents of circles.


• Solve problems involving common external tangents of circles.


• Solve problems involving externally tangent circles.


• Solve problems involving internally tangent circles.


• Common tangent

II.MultipleIntelligences

III.SpecialNeeds/Modifications

• This lesson focuses on problem solving.


• These notes will work for multiple intelligences and special needs students.


• The work that we are going to do to differentiate this lesson is to be sure that the steps to working through the
  problems are clear and understood.


• List out these steps as you teach the lesson. Request that the students copy these notes into their notebooks.


• Define common internal tangent.


• Define common external tangent.


• Steps to common External Tangents


• 
  
  
  
  1. Label the diagram.
  
  
  
  


• 
  
  
  
  2. Draw a line segment that joins the centers of the two circles.
  
  
  
  


• 
  
  
  
  3. Draw in the perpendicular segments.
  
  
  
  


• 
  
  
  
  4. Look for any polygons – Example = rectangle.
  
  
  
  


• Steps to Common Internal Tangents


• 
  
  
  
  1. Look for similarity. Here in Example 2, there are similar triangles.
  
  
  
  


• “Who can we find the length of x? Think back to our work on similar triangles.”


• Lead students to discover working with ratios.


• 
  
  
  
  2. Then we can find the length of the hypotenuse of the two triangles to identify the distance between the two
     circles.
  
  
  
  


• Use the Pythagorean Theorem to do this.


• Intersecting circles- define internally and externally tangent


• Walk through each example with the students. Rely on previously learned material from this lesson.

IV.AlternativeAssessment

• Be sure that the students are making the connections between the circles, perpendicular segments and where
  polygons and right triangles can help them in solving each problem.


• The students need to combine previously learned material to be successful with this lesson.


• Review information and skills when necessary.

Chapter 4. Geometry TE - Differentiated Instruction