A Medley of Post-Euclidean Theorems (extremely difficult)
The more well-known name for Theorem 110
What is Ceva's Theorem?
Define betweenness of points, i.e. A~B~C.
A, B, C are collinear and AB + BC = AC.
The number of tests we've had on Monday
What is 2?
Who are Saccheri and Legendre?
The city / town in which Ms. Bernstein lives
Where is Cambridge?
The three points of intersection of the adjacent trisectors of the angles of a triangle form a ________ triangle. (Theorem 131)
What is equilateral?
2 points are on opposite sides of a line if...
The segment with those 2 points as endpoints intersects the line
The number of tests we've had on Wednesday
What is 6?
The name of the Russian (not Hungarian) man who discovered Hyperbolic Geometry (hint: he was mentioned in a song Ms. Bernstein sang at Hancock)
Who is Lobachevsky?
What is the Commonwealth School and Harvard University?
The name of the man who discovered Theorem 131
If the sum of the measures of two angles is 90, then the angles are called _______, and each is called a _______ of the other.
What is complementary; complement?
The number of tests we've had on Tuesday
What is 3?
Who is Frederich Gauss?
The math organization founded by Ms. Bernstein (hint: the + name of city + math + some shape)
What is the Cambridge Math Circle?
The 3 centers of a triangle that are collinear
What are the orthocenter, the circumcenter, and the centroid?
Given 2 points A and B on a circle with center P, define the minor arc AB.
The minor arc AB is comprised of all points on the circle in the interior of angle APB.
The number of tests we've had on Friday
What is 0?
The name of the man who we base our axioms off of
Who is Hilbert?
A language besides English that Ms. Bernstein speaks fluently
What is Russian?
The name of the line containing the three collinear centers of a triangle
What is the Euler Line?
The more formal name for kissing angles
What are vertical angles?
The 2 tests that we got to choose when to take
What are the Chapter 4 test and the Sections 3.1 and 3.2 test?
The father of the man who invented Axiomatic Geometry against the advice (and essentially begging) of his father
Who is Nikos Bolyai?
The problem that Ms. Bernstein's mother told Ms. Bernstein when she was a child (hint: it was on the midyear)
Let L be a line, P a point not on L, Q another point not on L on the same side of L as P. What is the point R on L s.t. PR + RQ is less than PX + XQ (x is any point other than R not on L)?