The Defected Category
What is Euclidean Geometry?
The term used to describe when 3 lines (such as perpendicular bisectors, medians, angle bisectors, altitudes) intersect at 1 point
What is concurrent?
De Morgan's law
What is -(p and q) = -p v -q?
The Greek who wrote the Elements
Who is Euclid?
Theorem 11
If D is in the interior of angle BAC, then ray AD intersects segment BC.
The types of shapes in which we've proved defect is additive
What are triangles and convex quadrilaterals?
The intersection point of a triangle's medians
What is the centroid?
Negation of: p implies q
What is p and -q
The man who wrote our textbook (former Commonwealth teacher who died a decade ago)
Who is Farhad Riahi?
Theorem 72 (Hint: out of place in a very specific way)
A quadrilateral is convex if and only if the diagonals intersect.
The geometry in which the defect of a triangle is greater than or equal to 0.
What is neutral geometry?
The intersection point of the perpendicular bisectors of the sides of a triangle
What is the circumcenter?
The 2 types of logic we've studied in Geometry Advanced (both start with P.)
What are propositional and predicate?
The guy who wrote the proof of the bridge of donkeys (his name sounds like a rambunctious Commonwealth senior)
Who is Pappus?
A triangle is equilateral if and only if it's equiangular.
The geometry in which the defect of a triangle is greater than 0.
What is hyperbolic geometry?
What is the incenter?
Negation of: For every line there is at least one point not lying on it.
What is "There exists a line such that no point isn't lying on it."
The mathematician who rewrote the Euclidean Parallel Postulate into its more modern version (given a line, point not on line, etc.)
Who is Playfair?
Theorem 26 (the first one of Chapter 4)
Every angle has a unique bisector.
The geometry in which the defect of a triangle is less than 0.
What is elliptic geometry?
The intersection point of the altitudes of a triangle
What is the orthocenter?
The converse, the inverse, the contrapositive, the converse of the inverse, the inverse of the contrapositive, the converse of the contrapositive, and the converse of the inverse of the contrapositive of this statement: p implies q (you get 30 seconds to say your statement).
What is q implies p, -p implies -q, -q implies -p, -q implies -p, q implies p, -p implies -q, and p implies q?
The man who invented Axiomatic Geometry against the advice (and essentially begging) of his father
Who is Janos Bolyai?
Theorem 48 (the first one about perpendicular lines and planes)
If a line L is perpendicular to lines L1 and L2 at a point P, then L is perpendicular to the plane determined by L1 and L2.