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:
“We cannot feel strongly toward the totally unlike because it is unimaginable, unrealizable; nor yet toward the wholly like because it is stale—identity must always be dull company. The power of other natures over us lies in a stimulating difference which causes excitement and opens communication, in ideas similar to our own but not identical, in states of mind attainable but not actual.”
—Charles Horton Cooley (1864–1929)
“If triangles had a god, they would give him three sides.”
—Charles Louis de Secondat Montesquieu (1689–1755)