I"ve looked in a historicsweetsballroom.com publication that an isosceles triangle contends least two congruent sides. I also know the the native "at least" average this symbol: $\ge$, which method "is better than or same to" or "is no less than." This acquired me reasoning that equilateral triangle can likewise be isosceles triangles, but is that true?



An equilateral triangle is one with three equal sides. An isosceles triangle is one with two same sides.

You are watching: If a triangle is equilateral then it is

Therefore, every equilateral triangle is isosceles, but not every isosceles triangle is equilateral.

So far, so book. However, according to Wikipedia the definition of one isosceles triangle occasionally specifies the it must have actually two and only two equal sides. Under that (uncommon) definition, an it is provided triangle, having three equal sides, would certainly of course no be isosceles.

$\begingroup$ Exactly, yet please keep in mind the "uncommon definition" i in mine updated answer. $\endgroup$
$\begingroup$ Yes, under the definition you gave, every equilateral triangle is isosceles. $\endgroup$
NB: ns am presenting this answer together a framework challenge. The primary an ideas behind this price is come make much more permanent some of the comment left in response to the question and other answers, as well as to incorporate some principles from a currently deleted answer.

The prestige of Definitions

historicsweetsballroom.comematics is a human endeavor. The indigenous we usage to define historicsweetsballroom.comematical concepts are a human invention, thus it is necessary to identify that different humans might use the exact same word to describe different ideas, or different words to describe the same idea. As soon as one is trying to know a historicsweetsballroom.comematical idea presented by another, it is essential to know the presenter"s definitions. From the definitions, more deductions may be made.

For example, in the inquiry above, we have actually the definition:

Definition: an isosceles triangle is a triangle through at the very least two congruent sides.

An equilateral triangle has actually three congruent sides, and also three is "at least" two. Therefore, per this definition, every equilateral triangle must be isosceles.

See more: P A Line That Intersects Two Other Lines, Attention Required!

However, there are authors who give a different meaning of isosceles triangles. Joel Reyes Noche notes that numerous primary college instructors specify an isosceles triangle to it is in one v exactly two congruent sides. Indeed, this is the meaning given through Euclid himself!:

Per this definition, no isosceles triangle is equilateral, and no it is provided triangle is isosceles.