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How to use the similar triangle method to solve the dynamic balance problem of the stressed object. What are its applicable conditions
If the object is subjected to three forces, then one of them is a constant force (usually gravity) and the other two are variable forces. The three forces form a triangle and another is a real triangle, which is then solved by a series of equations with similar corresponding sides proportional to each other
There are several proofs of similar triangles
Method 1 (preparatory theorem)
If a line parallel to one side of a triangle intersects with the other two sides (or the extension lines on both sides), the triangle formed is similar to the original triangle (this is the lemma for judging similar triangles, which is the basis for proving the following judgment method. The proof method of this lemma requires the proof of the proportion of parallel line segments)
Method 2
If the two angles of a triangle are equal to those of another triangle,
So the two triangles are similar. (AA)
Method 3
If the ratio of two corresponding sides of two triangles is equal and the angle between them is equal, then the two triangles are similar (SAS)
Method 4
If the ratio of the three corresponding sides of two triangles is equal, then the two triangles are similar (SSS)
Method 5 (definition)
Two triangles whose corresponding angles are equal and whose corresponding sides are proportional are called similar triangles
The inference of judging theorem of triangle similarity
Corollary 1: two isosceles triangles with equal apex or base angles are similar
Corollary 2: the waist and the base correspond to two proportional isosceles triangles
Corollary 3: two right triangles with an equal acute angle are similar
Corollary 4: a right triangle is divided into two right triangles which are similar to the original triangle
Corollary 5: if both sides of a triangle and the center line on one side are proportional to the corresponding part of another triangle, then the two triangles are similar
When to use the similar triangle to solve the problem in the analysis of force in physics
There are two ways to solve the problem of force in physics
1. When one of the three forces knows the magnitude and direction (eg gravity), one force knows the direction, and the other force changes its magnitude and direction, the triangle of force
2. When one of the three forces knows its magnitude and direction (eg gravity), and the other two forces change their magnitude and direction, similar triangles are used
Happy study
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