Q: What criteria would show that two triangles are similar?

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To prove that two right triangles are similar, all you need to show is that one of them has one acute angle that's equal to one acute angle of the other one.

You can use the theorems like SSS, SSA to show that they are similar. For example if two triangles have the same 3 sides length or two side lengths equal and 1 angle equal they are similar. * * * * * That is congruent, not similar! Similar is a weaker requirement. All that is needed is that two corresponding angles are the same. Equivalently, the three corresponding sides are in the same proportion.

Nothing else, the angle-angle-side is sufficient to show the triangles are congruent. With two corresponding angles are equal, the third angles in the triangles by definition (the sum of the three angles in a triangle is 180o) must be equal making the triangles similar. If a corresponding pair of sides are also equal, then the other two corresponding pairs of sides will be equal.

The answer depends on what is already known about the two triangles.

All equilateral triangles are acute triangles, since all the angles are less than 90 degrees.

Related questions

Yes, AAA is a way to show that triangles are similar. Note, however, that AAA is not a way to show that triangles are congruent.

Yes.

To prove that two right triangles are similar, all you need to show is that one of them has one acute angle that's equal to one acute angle of the other one.

You can use the theorems like SSS, SSA to show that they are similar. For example if two triangles have the same 3 sides length or two side lengths equal and 1 angle equal they are similar. * * * * * That is congruent, not similar! Similar is a weaker requirement. All that is needed is that two corresponding angles are the same. Equivalently, the three corresponding sides are in the same proportion.

Recall that two triangles are similar if one is simply a larger or smaller version of the other. So if you can make one bigger or smaller (this is called dilating) so that it looks exactly the same as another (and would fit exactly if moved with a congruence transform), then this would show similarity.

You either show that the corresponding angles are equal or that the lengths of corresponding sides are in the same ratio.

Nothing else, the angle-angle-side is sufficient to show the triangles are congruent. With two corresponding angles are equal, the third angles in the triangles by definition (the sum of the three angles in a triangle is 180o) must be equal making the triangles similar. If a corresponding pair of sides are also equal, then the other two corresponding pairs of sides will be equal.

Once you have shown that two triangles are congruent you can use CPCTC (corresponding parts of congruent triangles are congruent) to show the congruence of the remaining sides and angles.

Angle side angle, side side side, hypotenuse length, side angle side, angle angle side.

You would have to check the criteria of the show, fill out all the nessecary paper work and you should be set.

You would have to check the cat criteria of the show. Usually when showing an animal in a "Cat" or "Dog" show, it is the best traits of the breed that would win the prize....

The answer depends on what is already known about the two triangles.