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Similarity Tests
Similarity Tests
In total, there are 3 possible tests for similarity.
In total, there are 3 possible tests for similarity.
- AA Test
- SSS Test
- SAS Test
A key difference between tests for congruency and similarity is that the S does not stand for same length but that the ratio of sides are proportional which is why you can't perform a ASA test for similarity. Proportionality must involve at least 2 pairs of sides (S).
A key difference between tests for congruency and similarity is that the S does not stand for same length but that the ratio of sides are proportional which is why you can't perform a ASA test for similarity. Proportionality must involve at least 2 pairs of sides (S).
(1) AA Test
(1) AA Test
The AA test states that any pair of triangles with 2 corresponding angles that are equal, are similar.
The AA test states that any pair of triangles with 2 corresponding angles that are equal, are similar.
(2) SSS Test
(2) SSS Test
The SSS test states that any pair of triangles with 3 pairs of corresponding sides that are proportional are similar.
The SSS test states that any pair of triangles with 3 pairs of corresponding sides that are proportional are similar.
(3) SAS Test
(3) SAS Test
The SAS test states that any pair of triangles with 2 pairs of corresponding sides that are proportional (i.e. Equal ratio) and the included angles between the sides are equal, the triangles will be similar.
The SAS test states that any pair of triangles with 2 pairs of corresponding sides that are proportional (i.e. Equal ratio) and the included angles between the sides are equal, the triangles will be similar.
The ratio of the corresponding sides is also known as the scale factor.
The ratio of the corresponding sides is also known as the scale factor.
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