The essential feature of similar triangles is "the same shape", and their sizes are not necessarily equal, which is an important difference from congruent triangles. In order to deepen students' understanding of the essence of similar triangles's concept, several pairs of similar triangles can be prepared in advance, so that students can observe or measure the relationship between the corresponding elements, and then intuitively draw the conclusion that the two triangles have the same shape, that is, the corresponding angles are equal and the corresponding sides are proportional.

Definition: A triangle with equal angles and proportional sides is called similar triangles.

The symbol "∽" is read as "similar to" and recorded as:

∽

, as shown.

In addition, similar triangles is a relay.

Note: When two triangles are similar, the letters representing the corresponding vertices are usually written in the corresponding positions.

2. The concept of similarity ratio

The ratio k of the corresponding sides of similar triangles is called similarity ratio (or similarity coefficient).

Note: ① The similarity ratio of two similar triangles is sequential.

if

and

The similarity ratio is k, then

and

The similarity ratio of is

.

② The similarity ratio of congruent triangles is 1, which also shows that congruent triangles is a special case of similar triangles.

3. Preliminary theorem: A straight line on one side of a parallel triangle intersects with the other two sides (or extension lines on both sides), and the triangle formed is similar to the original triangle.

∽

, as shown.