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

Narayana Triangle -- from Wolfram MathWorld

Johnson Triangle -- from Wolfram MathWorld

Using Wolfram, Alpha to Understand Mathematics

My girlfriend had this thought about what an Apex is in a triangle

Third Morley Triangle -- from Wolfram MathWorld

Triangle Function -- from Wolfram MathWorld

Mid-Arc Triangle -- from Wolfram MathWorld

Hexyl Circle -- from Wolfram MathWorld

Circle Packing -- from Wolfram MathWorld