Wednesday, December 5, 2012

Can an equilateral triangle also be isosceles?

According to the rule that an isosceles triangle has 2
sides that have equal lengths and 2 angles, formed with the equal sides, which have the
same measure, we'll conclude that any equilateral triangle could be considered as an
isosceles triangle.


The equilateral triangles present the
property of having all 3 sides of equal lengths and all 3 angles of equal measures.
Since the sum of the angles in a triangle is 180 degrees, it's easy to figure out the
measure of all 3 angles in the equilateral triangle.


Let's
note the measure of the angle as a:


a+a+a =
180


3a = 180


a =
180/3


a = 60


So, all 3 angles
have the measure of 60 degrees.


So, besides 2 equal lengths
of the sides, we'll have also 2 equal measures of the angles formed with the equal
sides.


Since all constraints of isosceles triangles have
been satisfied, we can state that all equilateral triangles are isosceles
triangles.

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