Similar triangles's judgment theorem is an important knowledge point in junior high school mathematics, as follows:

1, AA (angle) similarity theorem: two triangles are similar if their corresponding angles are equal. SSS similarity theorem: If three sides of two triangles are proportional, then the two triangles are similar. This theorem is very common in practical application.

2.SAS similarity theorem: If two sides of two triangles and their included angles are equal, then the two triangles are similar. This theorem is very useful in solving some geometric problems, because we only need to know two sides and the included angle between them to judge whether two triangles are similar or not.

3.ASA (Angle and Angle) Similarity Theorem: Two triangles are similar if their corresponding angles and non-included angles are equal. This theorem is very useful in some concrete problems. RHS (right-angled edge) similarity theorem: If an acute angle and a right-angled edge of two right-angled triangles are equal, then the two triangles are similar.

Relevant data of triangle stability

1, triangle stability means that a triangle has a unique property, that is, when the lengths of three sides of the triangle are determined, the shape and size of the triangle are fixed. This property is widely used in many engineering and architectural fields, such as the design of bridges, buildings and structural frames.

2. The stability of triangle comes from its geometric properties. In a triangle, the length of any one side can be determined by subtracting their greatest common divisor from the sum of the lengths of the other two sides. This means that the triangle will not be deformed or damaged even under the action of external force, because it has strong rigidity and stability.

3. In the field of architecture and engineering, triangular stability is widely used in structural design and supporting system. For example, the supporting structure of bridges usually adopts triangular frames, which can ensure the stability and bearing capacity of bridges. Triangular structures are also widely used in buildings to increase the stability and seismic capacity of buildings.