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Is it correct to say a triangle can be isosceles and equilateral?

Geometry question regarding triangles and classification based on side lengths. Got this question wrong on a test and wanted to check to see if I was correct in my assumption. 
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2 Answers

The terms isosceles and equilateral identify how many sides and how many angles are equal in a triangle so no, you would not use both terms for one triangle.
An isosceles triangle has two equal sides and two equal angles.
An equilateral triangle has three equal sides and three equal angles.


The fact that an isosceles triangle has two angles equal is a theorem, not part of the definition.
Talking with some math professors you could use an inclusive definition for an isosceles triangle which is a triangle that has at least two sides equal in which case that would include an equilateral triangle as an isosceles triangle. This is similar to a square also being a rectangle.
And so as mentioned for the angles being a theorem where the angles opposite the equal sides being equal would apply to both.
Definition: A triangle is isosceles if two sides are equal.
Definition: A triangle is equilateral if three sides are equal.
Every equilateral triangle is isosceles.
It is, however, quite possible for a triangle to be isosceles without being equilateral.