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
Read more about this topic: Similarity (geometry)
Famous quotes containing the words similar and/or triangles:
“Let the day perish wherein I was born, and the night in which it was said, There is a man child conceived.”
—Bible: Hebrew Job, 3:3.
A similar imprecation is found in Jeremiah 20:14-15.
“If triangles had a god, they would give him three sides.”
—Charles Louis de Secondat Montesquieu (1689–1755)