**Trinity Western University**

**Assignments**

**MATH 370: GEOMETRY 1 (**3 S.H.)** Fall 2016** **A:** MWF 1000-1050

**Professor: **R. Sutcliffe (NEU 17 ext 3213; rsutc@twu.ca)

*Hand in the bold assigned questions and any that appear here written out in full from Monday, Wednesday and Friday of a given week on the following Wednesday.*

**NOTE: **Each assignment is tentative until the end of that class day.

**NOTE: **Some questions mentioned in class as assignments may not be on this sheet, or there may be differences. This document is definitive.

I **September 5 - 9** Handins due Wednesday of Week II

Monday is Labour Day

1. W *1.1 (intro) * p6 # 6,9 *1.2 (modern) Read 1.3 (Finite) *p20 # 3 - 8, 11, 12, 13, 16, 1**8, 20, 23**

2. F *1.3-1.4 *p24 # 1 - 5, 7, 8, 10, 12, 14, **15**

II **September 12 - 16** Handins due Wednesday of Week III

3. M *1.4-1.5 Fano, Young, Pappus *p24 # **18, 19 **(Young)** **p30 # 1, 5,

4. W * Intro to Euclid *

5. F *Euclidian postulates and axioms*

**Prove the following:**

**a. A transversal intersects two parallel lines in the same angle.**

**b. Opposite angles are congruent.**

**c. Alternate angles are congruent**

**d. The measure of an exterior angle of a triangle is the sum of the measures of the two opposite interior angles.**

**e. The two acute angles of a right triangle are complementary.**

III **September 19 - 23** Handins due Wednesday of Week IV

6. M* Euclid continued*

**Prove the following**

**a. The converse of pons asinorum**

**b. Two alternate proofs of pons asinorum (Per the notes, or try something else)**

**c. That triangle similarity is an equivalence relation**

**d. Two triangles are similar if two pairs of sides in proprtion and their included angles congruent**

7. W * Euclid continued*

**Prove the following**

**a. Text p410 # S4, S10**

**b. If two triangles are similar with ratio k then the areas are in the ratio k**^{2}**.**

**c. The law of cosines for an obtuse triangle**

8. F *Euclid cont'd*

**a. Given two concentric circles and that the tangent segment to the inner one is inscribed in the outer one (i.e. just touches the outer one at its two ends) and has length 20m, what is the numerical value of the area between the two circles?**

**b. Prove that Heron's formula is equivalent to**

**c. Why is this version of the formula problematic for very small triangles?**

**d. How does the angle subtended by the chord on the closer circumference compare to the central angle?**

IV **September 26 - 30** Handins due Wednesday of Week V

9. M *Euclid cont'd*

**a. Given a circle with three chords mutually intersecting on the circle, two of them at right angles, show that the third is a diameter.**

**b. Prove the converse of the theorem on tangents and radii, namely given a radius of a circle is intersected by a line on the circle and at right angle to the radius, the line is a tangent to the circle.**

10. W *Euclid cont'd*

**a. Prove that the three medians of a triangle meet at a point.**

11. F *Constructions*

**Prove the validity of the following constructions:**

**a. constructing the perpendicular bisector of a segment**

**b. constructing the bisector of an angle**

**c. constructing a perpendicular from a point to a line**

V **October 3 - 7 **Handins due Wednesday of Week VI

12. M *Constructions Cont'd; Constructible Numbers 5.2*

**a. Prove the validity of the construction of a line through a point and parallel to a given line**

**Perform, describe, and illustrate the following constructions:**

**b. Given a segment, construct with it an equilateral triangle.**

**c. Given a circle, construct a second circle tangent to it and of half the radius.**

**d. Given a circle, construct a regular hexagon inscribed in it.**

**Prove E19 and E20** p219 # 1 - 8

13. W *Finish 5.2 Constructible Numbers; Start Advanced Euclidian Geometry*

**a. p 219 # 19, 21**

b. p163 # 1 - 12

14. F *Advanced Euclidian Geometry Cont'd*

VI ** October 10 - 14 **Handins due Wednesday of Week VII

Monday is Thanksgiving

15. W *4.1 ***p 163 # 21, 23**

16. F *4.1-4.2 *p 170 # 1-5, **13, 15,** 17, 18

VII **October 17 - 21** Handins due Wednesday of Week VIII

17. M 9-point circle, *Gergonne Point, Simpson line and Euler line *p176 # 1-5, **6, 10**

18. W **MIDTERM**

19. F *2.1 Transformations *p43 # 1-5, 7-24, **25, 26**

** Suppose f (x, y) --> (x + a, y + b) Under what circumstances (if any) is distance invariant?**

VIII **October 24 - 28** Handins due Wednesday of Week IX

20. M *2.2 Introduction to groups, dihedral groups * p51 # 1-4, **5**, 12,14, **18**, 20

21. W *finish 2.2 start 2.3*

22. F 2.3 *Euclidian motions in the plane *p59 # 1-7,9-11,13-15, **20 - 24,** 25

IX **October 31 - November 4** Handins due Wednesday of Week X

23. M *finish 2.3 start 2.4*

24. W *finish 2.4 start 2.5 *p68 #1-11,13-28 (as needed) **12, 29, 30**

25. F *finish 2.5 *p75 #1,3,5,8,11,13,**15, 19, 21, 26 and inverses for 1, 4**

X **November 7 - 11** Handins due Wednesday of WeekXI

26. M * 2.6 the group of Euclidian motions *p82 # 3,4,7,8,9,**11,**19,**21,23**

27. W* 2.8 *Plane similarities p 97 # **5**, 7, 10, 11, 12, **15**, 16, **18**

There is no class Friday due to reading break

XI **November 14 - 18** Handins due Wednesday of Week XII

28. M *6.1 Inversions *p248 # 1, 4, 7, 10, **11**, 12, 13, 15, 16, 18, 20, **23**

29. W *6.2 Properties of Inversions* p254 # 1, 3, 4, **11**, **12**, 14, **15**

30. F *6.3 Analytic Geometry of Inversions *p260 # 1-13 (odds), **15**, 17, 19, 23-29 odds, **31**

XII **November 21 - 25** Handins due Wednesday of Week XIII

31. M Finish *Analytic Geometry of Inversions*

32. W *7.1 Start Projective Geometry *

33. F *7.1 Projective Geometry *p278 #1-4, 6-18, **20**

XIII **November 28 - December 2** Handins due **MONDAY** of Week XIV

34. M *7.2-7.3 *p281 # 1-9, **10,** 11-15, **16, 17, 18 **p287 # 1-9, 10, **16, 17 **p299 # **2, 4, 5, 7**

35. W *Hyperbolic Geometry and Course eval *p368 # **20, 21, **22-27

36. F *Hyperbolic Geometry* p374 # 1-3, **5 (why),** 7-15 p378 #1-3, **4, 5, 6**

XIV **December 5 - 7** Any assignments after this point will not be for handing in

37. M Last class day *reviews*

Final Exam is TBA