MATH 7200 Discussion Points, Section 1.1

Euclidean Parallel Postulate.

Through a given point not on a line l there is exactly one line parallel to l.

Hyperbolic Parallel Postulate

Given a line l and a point P not on l, there exist at least two lines through P that are parallel to l.

George David Birkoff


See resources on main MATH 7200 page (or do Google Searches)

John Playfair

Playfair's Axiom

David Hilbert

Hilbert's Axioms



1.1 Angles and their Measurement

Pairs of Angles

Adjacent angles

Vertical angles

Supplementary angles

Complementary angles

Acute Angle

Obtuse Angle

Right Angle

Straight Angle


Notation Conventions

Theorem 1.1

Proof (b)

Proof (c)


EXAMPLE 1 --- This is the proof presented in the text. Are there any questions?


Problem Set 1.1