Mathematics 133
Notes from October 21, 2020, lecture session

The recording for this lecture is available online as  
http://math.ucr.edu/~res/math133-2020/Oct21.mp4  .

 Relevant directory files:
Here is a listing with comments on their significance.  These links are all clickable.
http://math.ucr.edu/~res/math133-2020/week3/geometrynotes02b.f13.pdf   The second  part of the second chapter of the course notes.   The lecture the remainder of Section II.3  and the material in Section II.4 up to the Isosceles Triangle Theorem  (Theorem II.4.1).
https://math.ucr.edu/~res/math133-2020/week3/compass-property.pdf  An alternate proof of Proposition II.3.1 corresponding to the argument in the lecture. 
https://math.ucr.edu/~res/math133-2020/week3/verifications.pdf   A summary of the work needed to show that the coordinate models for geometry satisfy the axioms for synhetic geometry.  This is included for the sake of completeness;  the portion which is relevant to this lecture involves the axioms for linear and angular measurement.   The part involving linear measurement is worth reading as an example of the work needed to verify the synthetic axioms in the coordinatee model for Euclidean geometry.  However, the part involving angular measurement is considerably more complicated and may be skipped; you are not responsible for knowing the details, and for the purposes of this course it is enough to recognize that the axioms can be verified by arguments requiring material not covered in the course prerequisites.
https://math.ucr.edu/~res/math133-2020/week3/Whiteboard.oct21-1.png   Drawing which illustrates the definition of an angle and some related concepts.
https://math.ucr.edu/~res/math133-2020/week3/Whiteboard.oct21-2.png   Drawings of objects often called 0 and 180 degree angles; these are NOT angles in the sense of our definition.  
https://math.ucr.edu/~res/math133-2020/week3/Whiteboard.oct21-3.png   Drawing for a synthetic proof of the Geometric Trichotomy Principle (Proposition II.3.6).  
https://math.ucr.edu/~res/math133-2020/week3/Whiteboard.oct21-4.png   Drawing for the Protractor Postulate which illustrates the need for restricting to a half plane determined by a line BC. 
https://math.ucr.edu/~res/math133-2020/week3/Whiteboard.oct21-5.png   Reminder for the need to distinguish between stating that two angles are the identical plane figures and stating that two angles have the same angular measure.
https://math.ucr.edu/~res/math133-2020/week3/Whiteboard.oct21-6.png https://math.ucr.edu/~res/math133-2020/week3/Whiteboard.oct21-7.png       Drawings for the interpretation of the Geometric Trichotomy Principle in terms of comparing angle measurements.
https://math.ucr.edu/~res/math133-2020/week3/trianglecongruence.pdf   Proofs that any one of the Triangle Congruence Postulates (SAS, ASA, SSS) implies the other two.  The statement of this result should be understood, but you are not responsible for knowing the proofs.
https://math.ucr.edu/~res/math133-2020/week3/Whiteboard.oct21-8.png https://math.ucr.edu/~res/math133-2020/week3/Whiteboard.oct21-9.png       Restatement about which conclusions are valid and which are usually not valid if you rearrange the ordering of the vertices in the statement rABC  @  rDEF.
https://math.ucr.edu/~res/math133-2020/week3/vert-angles.pdf   A proof of the Vertical Angle Theorem (attributed to Thales) using input from linear algebra.  You should understand this argument well enough to explain it correcty to another student in the class.
https://math.ucr.edu/~res/math133-2020/week3/math133hw02.pdf   List of the strongly recommended homework assignments for Chapter II.  This listing includes assignments for the previous two lectures and for the October 26 lecture.   Problems at roughly comparable levels of difficulty can be expected on quizzes and examinations.