Similar triangles's proportional formula, also called similarity formula, is an important formula commonly used in structural graphics, geometry and other disciplines. Mainly used to compare the proportional relationship between two similar triangles. Similar triangles's proportional formula can be expressed as follows: if two triangles ABC and A'B'C' are similar, there are three groups of ratios with equal numerator and denominator, namely: AB/A'B'=BC/B'C'=AC/A'C'
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(1) A straight line parallel to one side of a triangle intersects with the other two sides (or extension lines of both sides), and the triangle formed is similar to the original triangle;
(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, then two triangles are similar (in short, three sides are proportional and two triangles are similar);
(4) If two angles of two triangles are equal (or three angles are equal), then two triangles are similar (in short, two angles are equal and two triangles are similar).
The idea of proving the similarity of triangles: the idea of judging the similarity of two triangles;
1) First, find two pairs of equal internal angles (parallel lines find parallel lines), because this condition is the simplest;
2) First, find a pair of equal internal angles to see whether the two sides of the included angle are directly proportional;
3) If no corresponding angles are equal, only consider whether the corresponding three groups of edges are proportional;
Equal ratio transition method (equal ratio substitution method)
When the triangle can't be determined by the three-point setting method, and there is no equal ratio line segment substitution, the equal ratio substitution method can be considered, that is, the proportional bridge of the third group of line segments can be considered, that is, through the in-depth analysis of the known conditions or figures, the ratio equal to a certain ratio can be found in the verification conclusion and substituted, and then the triangle can be determined by the three-point setting method.