Isosceles Right Triangles

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Objective

Students will be able to learn about the ratios of the sides of isosceles right triangles, and then practice working with all of the special right triangles.

Big Idea

Students discover the ratio of the sides of all 45-45-90 degree triangles, and then practice working with all of the special right triangles.

Establishing the Pattern for 45, 45, 90 Triangles

5 minutes
IsoscelesRightTriangles_EstablishthePattern_Narrative (2).pdf page 1

Special Cases

10 minutes
IsoscelesRightTriangles_SpecialCases_Narrative.pdf page 1
IsoscelesRightTriangles_SpecialCases_Narrative.pdf page 2

Practice with Special Right Triangles

25 minutes

At this point, I announce that I’d like to use the remainder of the class period to pull together all of the special right triangles: the common Pythagorean triplets, the  triangles, and the 45o, 45o, 90o triangles.  To this end, I hand out the Practice with Special Right Triangles worksheet, and ask that the students work in their groups to fill in the lengths of the missing segments.  I suggest, as in a previous lesson with special right triangles, that they attempt to do the problems without doing any work (i.e. without solving for sides using the Pythagorean Theorem).  They should instead try to rely on their knowledge of the special right triangles.

Reflection

5 minutes

I pass out a “ticket out the door” on which I ask:

 

           1.  What is meant by the term “Pythagorean triplet”?  What triplets do you know?

 

           2.  What facts do you know about all  triangles?

 

           3.  What facts do you know about all isosceles right triangles?

 

The students’ answers to these questions will be the basis of the beginning of the next day’s lesson.