Similar Triangles
Two triangles and are said to be similar if either of the following equivalent conditions holds:
1. They have two identical angles, which implies that their angles are all identical. For instance:
- is equal in measure to, and is equal in measure to . This also implies that is equal in measure to .
2. Corresponding sides have lengths in the same ratio:
- . This is equivalent to saying that one triangle (or its mirror image) is an enlargement of the other.
3. Two sides have lengths in the same ratio, and the angles included between these sides have the same measure. For instance:
- and is equal in measure to .
When two triangles and are similar, one writes
or
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Famous quotes containing the words similar and/or triangles:
“So-called professional mathematicians have, in their reliance on the relative incapacity of the rest of mankind, acquired for themselves a reputation for profundity very similar to the reputation for sanctity possessed by theologians.”
—G.C. (Georg Christoph)
“If triangles had a god, they would give him three sides.”
—Charles Louis de Secondat Montesquieu (1689–1755)