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

(2) If two sides of a triangle are proportional to two sides of another triangle and the included angle is equal, then two triangles are similar (abbreviated as: two sides are proportional and the included angle is equal, and two triangles are similar. )

(3) If three sides of a triangle are proportional to three sides of another triangle, two triangles are similar (abbreviated as: three sides are proportional, 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.

Similar triangles's property theorem;

(1) similar triangles have equal angles.

(2) The corresponding sides of similar triangles are proportional.

(3) The ratio of the corresponding high line, the ratio of the corresponding middle line and the ratio of the corresponding angular bisector in the similar triangles are all equal to the similarity ratio.

(4) The perimeter ratio of similar triangles is equal to the similarity ratio.

(5) The area ratio of similar triangles is equal to the square of the similarity ratio.

Transitivity of similar triangles

If △ ABC ∽△ a1b1,△a 1c 1∽△a2b2c 2, then △ABC∽A2B2C2.