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Can an equilateral triangle also be isosceles?

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estanbuen | Student | eNoter

Posted September 25, 2010 at 3:27 PM via web

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Can an equilateral triangle also be isosceles?

Tagged with geometry, math, triangle

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william1941 | College Teacher | Valedictorian

Posted September 25, 2010 at 6:16 PM (Answer #1)

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In an equilateral triangle all the three sides of the triangle are of the same length. If only two sides are equal in length the triangle is called isosceles and if all the three sides are of different lengths it is called a scalene triangle.

If the three sides of a triangle are equal, it is necessary that if any two of the sides are chosen they are also of the same length. Thus equilateral triangles are isosceles. This does not imply, though, that all isosceles triangles have to be equilateral.

Therefore an equilateral triangle can be isosceles.

 

 

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neela | High School Teacher | Valedictorian

Posted September 25, 2010 at 3:54 PM (Answer #2)

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In an equilateral triangle all three  sides are equal.

In an isosceles triangle two sides are equal.

So in an equilateral triangle any two sides are equal. So the equilareral triangles are also isosceles.

In an equilateral tringle all 3 angles are equal  and each of them must be equal to 60 degree only. And all angles are acute.

In an isosceles triagle  all 3 angles are acute . Further, two  angles are acute and equal .

An equilateral angle has a maximum area for a given perimeter. Or  for a given area has the minimum permeter.

Foa a given perimeter, an isosceles triangle achieves its maxmum area when it becomes an quilateral area.

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krishna-agrawala | College Teacher | Valedictorian

Posted September 25, 2010 at 3:59 PM (Answer #3)

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A triangle is figure that is enclosed by three straight lines. Triangles are classified in many different ways, One such way of classification is according to the relative lengths of their sides.  In a scalene triangle all the three sides are of unequal length.  An isosceles triangle at least two sides have equal length.  In an equilateral triangle all three sides are of equal length.  Thus, every equilateral triangle is also an isosceles triangle, but every isosceles triangle is not an equilateral triangle.

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giorgiana1976 | College Teacher | Valedictorian

Posted September 25, 2010 at 7:25 PM (Answer #4)

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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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