Similarity theorems
The similarity theorems are propositions that set sufficient conditions that two triangles are similar . Many statements about geometry can be proven with the help of the similarity of triangles.
The four similarity theorems for triangles
The four similarity theorems for triangles are:
- Two triangles are similar to each other if they match at two (and thus three) angles . (W: W: W sentence)
- Two triangles are similar to each other if they match in all proportions of corresponding sides. (S: S: S phrase)
- Two triangles are similar to each other if they match at an angle and in the ratio of the adjacent sides. (S: W: S sentence)
- Two triangles are similar to each other if they match in relation to two sides and in the opposite angle of the larger side. (S: S: W sentence)
See also : Congruence Theorems
In the following four figures, two similar triangles ABC and A'B'C '- speaking clearly - are "nested".
Then every pair of side lengths in ABC is proportionally equal to the corresponding pair of side lengths in A'B'C '.
literature
- Hans Schupp: Elementary Geometry. UTB, Stuttgart 1977. ISBN 3-506-99189-2 , p. 144