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Someone correct me if I am wrong, but I don't believe triangles can be "equal", only congruent. The measurements can be equal, but not the triangle itself.

The triangle congruency postulates and theorems are:

Side/Side/Side Postulate - If all three sides of a triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

Angle/Side/Angle Postulate - If two angles and a side included within those angles of a triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

Side/Angle/Side Postulate - If two sides and an angle included within those sides of a triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

Angle/Angle/Side Theorem - If two angles and an unincluded side of a triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

Hypotenuse/Leg Theorem - (right triangles only) If the hypotenuse and a leg of a right triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

Q: What is the triangle equality theorem?

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The Pythagorean Theorem is not a triangle. It's a statement that describes a relationship among the lengths of the sides in any right triangle.

The circumcenter of a triangle is equidistant from the vertices of a triangle.

A right angle triangle

Yes

You use Lami's theorem wen you triangle of forces to calculate the sides of the triangle or the angles opposite to a side.

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The isosceles triangle theorem states that if two sides of a triangle are congruent, the angles opposite of them are congruent. The converse of this theorem states that if two angles of a triangle are congruent, the sides that are opposite of them are congruent.

The theorem that states every triangle's angles add up to 180 degrees

Pythagoras theorem will always work with a right-angled triangle.

The Pythagorean Theorem is not a triangle. It's a statement that describes a relationship among the lengths of the sides in any right triangle.

Yes

A right angle triangle

The circumcenter of a triangle is equidistant from the vertices of a triangle.

The triangle inequality theorem states that any side of a triangle is always shorter than the sum of the other two sides.

You use Lami's theorem wen you triangle of forces to calculate the sides of the triangle or the angles opposite to a side.

The Pythagorean theorem uses the right triangle.

Pythagoras's Theorem is used to determine if a triangle is a right triangle or not.

any right triangle