An equilateral triangle is one with three equal sides. One isosceles triangle is one with two equal sides.
You are watching: All equilateral triangles are also isosceles triangles
Therefore, every it is provided triangle is isosceles, however not every isosceles triangle is equilateral.
So far, therefore book. However, follow to Wikipedia the definition of an isosceles triangle sometimes specifies that it must have two and also only two same sides. Under that (uncommon) definition, an it is intended triangle, having three equal sides, would of course not be isosceles.
$\begingroup$ Exactly, however please keep in mind the "uncommon definition" i in mine updated answer. $\endgroup$
$\begingroup$ Yes, under the definition you gave, every it is provided triangle is isosceles. $\endgroup$
NB: i am presenting this answer together a framework challenge. The primary motivation behind this answer is to make more permanent some of the comments left in response to the question and also other answers, as well as to incorporate some concepts from a now deleted answer.
The prominence of Definitions
mslsec.comematics is a human endeavor. The words we use to explain mslsec.comematical ideas are a person invention, thus it is necessary to recognize that different humans could use the very same word to define different ideas, or different words to explain the exact same idea. When one is make the efforts to know a mslsec.comematical idea gift by another, that is crucial to know the presenter"s definitions. Indigenous the definitions, further deductions may be made.
For example, in the question above, we have actually the definition:
Definition: one isosceles triangle is a triangle v at least two congruent sides.
An it is intended triangle has three congruent sides, and also three is "at least" two. Therefore, every this definition, every equilateral triangle must be isosceles.
See more: 2002 Nissan Altima Pcv Valve Location, Pcv Valve Removal And Install
However, there are authors who offer a different an interpretation of isosceles triangles. Joel Reyes Noche note that plenty of primary school instructors define an isosceles triangle to be one through exactly 2 congruent sides. Indeed, this is the definition given by Euclid himself!:
Per this definition, no isosceles triangle is equilateral, and also no it is intended triangle is isosceles.