"Congruent" means "same shape and size as the other one". So one thing
all by itself is never congruent. It needs something else to be congruent with.
An isosceles triangle is never congruent to a scalene triangle, sometimes congruent
to any other kind of triangle, and always congruent to another isosceles triangle that's
congruent to the first one.
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An isosceles triangle.
Isosceles triangle
An isosceles triangle has at least two congruent sides. An equilateral triangle has three congruent sides. So, an equilateral triangle is a special case of isosceles triangles. Since the equilateral triangle has three congruent sides, it satisfies the conditions of isosceles triangle. So, equilateral triangles are always isosceles triangles. Source: www.icoachmath.com
sometimes, but not always
If you mean an isosceles triangle then no because all triangles have no diagonals