Triangle -- from Wolfram MathWorld

A triangle is a 3-sided polygon sometimes (but not very commonly) called the trigon. Every triangle has three sides and three angles, some of which may be the same. The sides of a triangle are given special names in the case of a right triangle, with the side opposite the right angle being termed the hypotenuse and the other two sides being known as the legs. All triangles are convex and bicentric. That portion of the plane enclosed by the triangle is called the triangle interior, while the

Figurate Number Triangle -- from Wolfram MathWorld

Catalan's Triangle -- from Wolfram MathWorld

Using Wolfram, Alpha to Understand Mathematics

Mid-Arc Triangle -- from Wolfram MathWorld

Inner Vecten Triangle -- from Wolfram MathWorld

Outer Vecten Triangle -- from Wolfram MathWorld

Tessellation -- from Wolfram MathWorld

First Morley Adjunct Triangle -- from Wolfram MathWorld

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Inner Napoleon Triangle -- from Wolfram MathWorld

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Magog Triangle -- from Wolfram MathWorld