形似三角形的性质及其证明方法。(国外英文资料).doc

形似三角形的性质及其证明方法。(国外英文资料) The understanding of similar triangles The two triangles that correspond to the same angle and correspond to the sides are called similar triangles. Triangles that resemble each other are called similar triangles [Edit] the method of judging similar triangles Judge according to the characteristics of similar figures. (proportional to the sides and equal angles of the corresponding sides) 1. a line parallel to one side of a triangle intersects with the other side (or an extended line on both sides), forming a triangle similar to the original one; (this is a lemma for the determination of similar triangles, which is the basis for the proof of the following methods of decision. The proof method of this lemma needs to be proved by parallel lines and segments in proportion 2. if the two angles of a triangle correspond to the two angles of another triangle, the two triangles are similar; 3. if the ratio of the two sets of two triangles is equal, and the corresponding angles are equal, then the two triangles are similar; 4. if the ratio of the three sets of two triangles is equal, then the two triangles are similar; 5. equal angles equal to two triangles corresponding to the sides are called similar triangles (as defined) Absolutely similar triangle 1., two congruent triangles must be similar. 2. two isosceles right triangles must be similar. (two isosceles triangle, if they are equal, then the two corner vertex or isosceles triangles are similar.) 3., two equilateral triangles must be similar. Similarity judgment theorem of right triangle A two right triangle similar in proportion to a right angle side. 1. 2. right angled triangles are divided into two right triangles by the height of the bevel, similar to those of the original right triangle, and are divided into two right angled triangles. Projective theorem A judgment theorem for triangles; a corollary A corollary: equal angle or the bottom corner of the two isosceles triangle similarity. Corol