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Q: If the vertex angles of two isosceles triangles are congruent are the triangles always similar?

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No

No, congruent triangles are always similar but similar triangles and not always congruent. Imagine that similar triangles can be created on a copy machine enlarge and shrink the image, turn it, even turn it over, the angles remain the same. A congruent triangle must be exactly the same as the original. Hope this helps!

No. A triangle is similar to one that is twice its size but the two are not congruent.

The relative angles are congruent

In an isosceles triangle, two angles, and therefore sides (Base Angle Theorem), are congruent. This does not mean that all isosceles triangles are also right triangles - there is only one (45, 45, 90 triangle).

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If you mean an isosceles triangle then no because all triangles have no diagonals

Yes, in similar triangles, the angles are always congruent, and the sides have the same proportions to each other.

No

No, congruent triangles are always similar but similar triangles and not always congruent. Imagine that similar triangles can be created on a copy machine enlarge and shrink the image, turn it, even turn it over, the angles remain the same. A congruent triangle must be exactly the same as the original. Hope this helps!

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

No. A triangle is similar to one that is twice its size but the two are not congruent.

Yes because the two sides of a triangle that are the same lenth are congruent.

Similar, YES. Congruent, NO.

The relative angles are congruent

Sometimes.

In an isosceles triangle, two angles, and therefore sides (Base Angle Theorem), are congruent. This does not mean that all isosceles triangles are also right triangles - there is only one (45, 45, 90 triangle).

If you mean you can "scale" two similar triangles so that they become congruent, then yes.The answer is Dilatedilate

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