Math 444/487 Geometry Week 3

Monday 10/13 - Friday 10/17
    444 Home Page

  1. Week 1: 9/29-10/03

  2. Week 2: 10/06-10

  3. Week 3: 10/13-17

  4. Week 4: 10/20-24

  5. Week 5: 10/27-31

  6. Week 6: 11/03-07

  7. Week 7: 11/10-14

  8. Week 8: 11/15-21

  9. Week 9: 11/24-28

  10. Week 10: 12/01-05

  11. Week 11: 12/08-12

Math 444 JSP Page

 

Monday 10/13 444

  • Assignment 2B due.
  • Construction of segments from ratios
  • Similar triangles and right triangles
    • The Find the Intersection part of this sheet, proved that if line m is perpendicular to CD at D and line n is not perpendicular to CD at C, then m and n are not parallel.
    • It is each to see that if n is perpendicular to CD, then n is parallel to n. (If they met at point F, then triangle FCD would have angle sum > 180; also there would be two perpendiculars to CD through F. Both impossible.)
    • Put these two results together proves that for a point C not on a line m, there is exactly one line through C that is parallel to m. The is the famous Parallel Postulate. For details for this proof, read B&B, Theorem 13.
Assignment

Wednesday 10/15 444

  • Assignment 3A due. Link to Answers to 3.3 and 3.4.
  • Class Activity:
  • Similar right triangles (problem 3.1) and Pythagorean Theorem
  • Review:
    • Strategy for proviing. State what you are proving. Write given and draw picture at the start. Write what to prove at the end with a picture. Find a path from one to the other.
    • Be careful to notice if and only if statements when one proves "a set equals ... another set".
    • Answers to problems 2.6 and 3.2.
Assignment
  • Practice the ratio problems, B&B pp. 64-65.
  • Study the rest of Chapter 3 in B&B
  • Assignment 3B due Wednesday 10/22

Wednesday 10/15 487 Lab 3

Lab 3 - Carpenter theorem (bring GTC Chapter 4)

Answer questions on the lab sheet on separate sheet and show to instructor.

Friday 10/17 444

QUIZ 1: The quiz will take all or most of the class period. It will include questions, constructions, and problems based on work through 10/15.

  • Theorems and problems from Chapters 1, 2, 3 in B&B, also pp. 105-111
  • Straightedge constructions from B&B, pp. 173-183 and from assignments
  • Constructions and theorems from lab and GTC
  • Notes and class activities documented on the class web site.
  • Problems from Assignments 1A through 3A
Assignment (for quiz)
  • Review B&B Chapers 1, 2, 3 + straghtedge and compass onstructions in chapter 6.
  • Constructions and concepts from Lab and Assignments. Perpendicular bisectors and circumcircle, angle bisectors and inscribed circles (an excircles).
  • Notes and Class Activities from M444 website.
  • Definition of line reflection and line symmetry from Brown and notes.