Q: How can two triangles be proven similar?

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Two equilateral triangles are always similar!

They are said to be similar but not congruent triangles.

for two similar triangles , their corresponding angles are equal.

Nope. You must know what it means to be similar. It means that ALL three angles are the same between two triangles. That been said, you can take any two random triangles, it's very likely that they are NOT similar.

Such triangles are similar.

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Two equilateral triangles are always similar!

They are said to be similar but not congruent triangles.

Not always, sometimes two obtuse triangles are similar and sometimes they are not similar.

Yes. You can even have two triangles with two pairs of sides that are the SAME measure without the triangles being similar.

If the angles of two triangles are equal the triangles are similar. AAA If you have three angles on both triangles these must be equal for the triangles to be similar. SAS If you have an angle between two sides and the length of the sides and the angle are the same on both triangles, then the triangles are similar. And SSS If you know the three sides

for two similar triangles , their corresponding angles are equal.

The triangles are similar, but not necessarily congruent.

The term for two triangles that are congruent after a dilation is similar.

They're similar triangles.

Nope. You must know what it means to be similar. It means that ALL three angles are the same between two triangles. That been said, you can take any two random triangles, it's very likely that they are NOT similar.

It is given that two triangles are similar. So that the ratio of their corresponding sides are equal. If you draw altitudes from the same vertex to both triangles, then they would divide the original triangles into two triangles which are similar to the originals and to each other. So the altitudes, as sides of the similar triangles, will have the same ratio as any pair of corresponding sides of the original triangles.

yes