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Are all isosceles triangles equilateral?

Answer 1

No.
Isosceles triangles are those that have two sides to be of equal length, while equilateral triangles are those that have all three sides of equal length.

Theorem There exist isosceles triangles that are not equilateral.

Proof A triangle with a base of 10 cm and two other sides each of 20 cm is isosceles, but not equilateral.

This counter example proves that not all isosceles triangles are equilateral.

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Answer 2

Wyatt Anderson

No, not all isosceles triangles are equilateral. Isosceles triangles have at least two sides that are of equal length, but equilateral triangles have all three sides of equal length. So while an equilateral triangle is a special case of an isosceles triangle, not all isosceles triangles have all sides equal in length, thus they are not necessarily equilateral.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.