You mean triangle similarity, right? It is often used when doing several problems of triangle similarity judgment theorem.

Similar triangles's judgment theorem;

(1) A straight line parallel to one side of a triangle intersects with the other two sides to form a triangle similar to the original triangle.

The simple description is that two angles are equal and two triangles are similar.

(2) If two sides of a triangle are proportional to two sides of another triangle, and the included angles are equal, then the two triangles are similar.

(In short, the two sides are proportional, the included angle is equal, and the two triangles are almost the same. )

(3) If three sides of a triangle are proportional to three sides of another triangle, then the two triangles are similar.

In short, three sides are proportional and two triangles are similar. )

(4) If two angles of two triangles are equal respectively (or three angles are equal respectively), then two triangles are similar.

Theorem for judging the similarity of right triangle;

(1) The right triangle is divided into two right triangles by the height on the hypotenuse, which is similar to the original triangle.

(2) If the hypotenuse and a right-angled side of one right-angled triangle are proportional to the hypotenuse and a right-angled side of another right-angled triangle, then the two right-angled triangles are similar.