Pythagoras' Theorem.
The square on the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides.
Euclid's proof:
Another proof:
The medians of a triangle are concurrent at the centroid.
The altitudes of a triangle are concurrent at the orthocentre.
The internal bisectors of the angles of a triangle are concurrent at the centre of the incircle.
The perpendicular bisectors of the sides of a triangle are concurrent at the centre of the circumcircle.
Pappus' Theorem:
Pascal's Theorem:
The Simson Line
The Nine-Point Circle
The Euler Line
Morley's Theorem
The "outer" internal angle trisectors of a triangle intersect to form an equilateral triangle.
Napoleon's Theorem
