What is the minimum condition for two triangles to be similar?

Two triangles with equal triangles and proportional sides are called similar triangles.

Similar triangles's judgment methods are:

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

If two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar.

If the ratio of two sets of corresponding sides of two triangles is equal and the corresponding included angles are equal, then the two triangles are similar.

Two triangles are similar if the ratio of their three corresponding sides is equal.

Theorem for judging the similarity of right-angled triangles 1: The hypotenuse is similar to two proportional right-angled triangles corresponding to one right.

Theorem 2: A right triangle is divided into two right triangles by the height on the hypotenuse, which is similar to the original right triangle, and the two right triangles are similar.

Height theorem of right triangle

The nature of similar triangles

1. The ratio of all corresponding line segments (corresponding height, corresponding centerline, corresponding angle bisector, circumscribed circle radius, inscribed circle radius, etc.). ) is equal to similarity ratio in similar triangles.

2. The ratio of similar triangles perimeter is equal to similarity ratio.

3. The ratio of similar triangles area is equal to the square of similarity ratio.