An equilateral triangle is one with three equal sides. An isosceles triangle is one v two same sides.
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Therefore, every it is provided triangle is isosceles, yet not every isosceles triangle is equilateral.
So far, so book. However, according to Wikipedia the an interpretation of one isosceles triangle occasionally specifies the it must have actually two and only two same sides. Under that (uncommon) definition, an equilateral triangle, having three equal sides, would certainly of course no be isosceles.
$\begingroup$ Exactly, yet please keep in mind the "uncommon definition" paragraph in my updated answer. $\endgroup$
$\begingroup$ Yes, under the meaning you gave, every it is intended triangle is isosceles. $\endgroup$
NB: i am presenting this answer together a frame challenge. The primary motivation behind this price is to make much more permanent few of the comment left in solution to the question and also other answers, and also to incorporate some principles from a now deleted answer.
The importance of Definitions
thedesigningfairy.comematics is a human being endeavor. The indigenous we use to explain thedesigningfairy.comematical principles are a person invention, for this reason it is important to acknowledge that various humans might use the exact same word to define different ideas, or various words to describe the very same idea. When one is trying to understand a thedesigningfairy.comematical idea presented by another, that is important to recognize the presenter"s definitions. From the definitions, further deductions might be made.
For example, in the concern above, we have the definition:
Definition: one isosceles triangle is a triangle through at least two congruent sides.
An it is provided triangle has three congruent sides, and also three is "at least" two. Therefore, every this definition, every it is provided triangle need to be isosceles.
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However, there space authors who offer a different an interpretation of isosceles triangles. Joel Reyes Noche note that countless primary institution instructors define an isosceles triangle to be one v exactly two congruent sides. Indeed, this is the an interpretation given by Euclid himself!:
Per this definition, no isosceles triangle is equilateral, and no equilateral triangle is isosceles.