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The ideas in this geometry lesson are taken from the Geometry ebook that I sell at MathMammoth.com. This lesson plan does not contain all the problems the Geometry ebook does.


Equilateral and isosceles triangles
Free geometry lesson plan from HomeschoolMath.net

A triangle whose all sides are equal is called
an equilateral triangle. "Equi" refers to
something same or equal; "lateral" refers to
sides.  Think of it as the "same-sided triangle".
      A triangle where at least two sides are
equal (and even the third can be) is called
an isosceles triangle.  Think of it as the
"same-legged triangle", the legs being the
two sides that are are the same.


    


Example problem types

1.  Draw an isosceles triangle (a triangle that has two equal sides).  Start out by drawing the two sides that have equal measure and draw the third side last.  Use a ruler to make sure they are equal.

2.   Make a guess about the angles in an equilateral triangle: ______________ 
Then measure the angles in the equilateral triangles above.  What do you notice?  
ALL the angles are _______ degrees.
Based on that fact, draw an equilateral triangle.  You can choose the length of the sides.

                        

An isosceles triangle has two angles that have the same measure. 
They are called the base angles,  The remaining angle is called the top angle.

4.  a) Draw an isosceles triangle whose base angles are 40.  What is the top angle?  The length of the sides can be any.
     b) Draw an isosceles triangle whose base angles are 75.  What is the top angle?  Again the length of the sides can be any.

6.  a)  Is it possible to have an equilateral right triangle?  Why?  If so, draw one.
     b)  Is it possible to have an equilateral obtuse triangle? Why?  If so, draw one.
     f)  Is it possible to have an isosceles acute triangle? Why?  If so, draw one.
     

7. Calculate the angles.  Don't measure, because the pictures are not exact.  Note especially if the triangle(s) are equilateral or isosceles.

[Pictures available in the ebook]

 

New terms to remember:

  • an equilateral triangle
  • an isosceles triangle 
  • base angles
  • top angle

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