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:
“The history of all Magazines shows plainly that those which have attained celebrity were indebted for it to articles similar in natureto Berenice—although, I grant you, far superior in style and execution. I say similar in nature. You ask me in what does this nature consist? In the ludicrous heightened into the grotesque: the fearful coloured into the horrible: the witty exaggerated into the burlesque: the singular wrought out into the strange and mystical.”
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“If triangles had a god, they would give him three sides.”
—Charles Louis de Secondat Montesquieu (1689–1755)