Yes if you mean in degrees
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Similar, YES. Congruent, NO.
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
Yes because the two sides of a triangle that are the same lenth are congruent.
If you mean an isosceles triangle then no because all triangles have no diagonals
Yes, that's part of what the word congruent means. Not only do congruent triangles have the same shape they are of the same size, and you can move one of them over the other one so that it covers it exactly.Note that you cannot flip a triangle over and consider it conguent to another triangle.