an equilateral triangle has 3 congruent sides and angle measures.
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An isosceles triangle has two sides the same length. An equilateral has all 3 sides the same length. A scalene triangle doesn't have any sides that are the same length.
The interior angles of any triangle (not traingle) always sum to 180 degrees. Whether or not it is equilateral (not eguilateral) is irrelevant.
Upright triangle: spirit, divinity According to ancient beliefs, an upright equilateral triangle, with one point at the top and two at the base, is a male and solar symbol representing spirit, divinity, fire, life, prosperity and harmony. In contrast, the reversed triangle is female and lunar, representing mother earth, water, rain and grace. In Christianity and Judaism, a triangle is often used as a symbol for God and the holy trinity, and in magic it was seen as representing the element fire (with a downward meaning water). When upright and downward triangles are put together, they form the Star of David and symbolize balance and knowledge. Having the symbol in your life can be used to denote a connection with, or interest in, spirit and the spiritual realm. Upside down triangle: The alchemical/magical symbol for water is an inverted triangle, symbolizing downward flow. The downward pointing triangle is an ancient symbol of femininity, being a representation of female genitalia.
The difference between plane and spherical triangles is that plane triangles are constructed on a plane, and spherical triangles are constructed on the surface of a sphere. Let's take one example and run with it. Picture an equilateral triangle drawn on a plane. It has sides of equal length (naturally), and its interior angles are each 60 degrees (of course), and they sum to 180 degrees (like any and every other triangle). Now, let's take a sphere and construct that equilateral triangle on its surface. Picture an "equator" on a sphere, and cut that ball in half through the middle. Set the top half on a flat surface and cut it into four equal pieces. Now if you "peel up" the surface of one of those quarters and inspect that triangle, it will have three sides of equal length, and will have three right angles. Not possible on a plane, but easy as pie on the surface of a sphere. Spherical trig is the "next step up" from plane trig.
Triangle