Homework for Mat 304 spring 2016
April 29 – Friday - EXAM at 8
April 27
April 25
April 23 Last day the third test can be given.
April 21
April 19 – Four students proved theorems. Discussed measures of intercepted arcs. Homework: Exercise 4.5 – 12, 16,
and 17. Third test stops with this homework. (“Locus” is an antiquated word for set.)
April 16 – Three students wrote problems on the board. Discussed circle theorems. Distributed optional bonus daily
grade ( they do NOT add into the point total of required points just extra daily points to replace hw or quiz grades.)
Homework: Define: Euler’s line, nine-point circle, excircle of a triangle, central angle, semicircle, minor arc and major
arc. Exercises 4.5 – 3 or 4 and 10 or 11.
April 14 –Returned area worksheets. Discussed ways of proving triangles similar. Discussed geometric mean, and
outlined the proof of number #15 in the exercises. Discussed circle vocabulary from section 4.5. Homework: Section
4.4 – prove 8 or 9 and 16. Work 13 and 14. Read section 4.5 through page 165. Prove: Caleb’s theorem - IF two
parallel lines are cut by a transversal corresponding angles are congruent.
April 12 – Returned homework proof collected and the scavenger hunt. Discussed measurement units. Collected the
area/perimeter worksheet. Homework: Read section 4 through the proof of Th 4.4.4. I expect you to convert in either
of the systems of measure discussed today using any units. But not between the two systems. Exercise 4.4 2 and 3.
April 8 – Scavenger hunt. Mary and Tucker wrote proofs on the board. Similar polygons were defined. Homework:
Section 4.2 – 22; Section 4.3 – 17, 18, and 22 define similar polygons.
April 6 – Kasie and Sarah wrote a theorem on the board. Area formulas were discussed. Linear measure was discussed.
Homework: Students must know English lengths (in, yd, mi) and Metric prefixes as well as basic area formulas. They
should convert units when asked. Section 4.3 – Tucker #3 (everyone else try it too), 12 and 14. Area handout is due by
Monday.
April 4 – Wrote an induction proof of Theorem 4.2.21. Homework: Define – altitude of a triangle and orthocenter;
incenter of a triangle and its inscribed circle.(practice these constructions on at least two kind of triangles. Practice
triangles are outside my office.) Complete previous proofs from section 4.2. KNOW Hero’s formula. Section 4.2 - #18
for all and # 21 for Caleb.
April 1 – Three students wrote proofs. Class discussion outlined two other proofs. Homework: Exercise 4.2 – Mary – 12
and Sarah – 14. Each student should try at least one of the two assigned to particular students. Then everyone work on
#16 as outlined during class.
March 30- Returned tests. Students selected a proof to hand in. Proved 4.2.13 in class. Homework: Exercises 4.2 Diane- 8, Kasie – 11, other students work on these two. If you have a problem assigned, work on the other one also.
Sarah’s Theorem – Diagonals of a kite are perpendicular. (everyone needs to prove this.)
March 25 – Chapter 4 discussion. Defined rectangle, kite, rhombus and square. Demonstrated an analytic proof.
Homework: Define – kite, rhombus, rectangle and square (parallelogram and trapezoid have already been discussed).
Exercises4.2 – 6, 9 (outlined in class – write it up).
March 23 – TEST
March 21 – Discussed possible form of test. Outlined the proof of #12. Began the discussion of Chapter 4. Prove
Corollary 4.2.3
March 18 – NO CLASS. Homework in Section 3.6 – problems 9 and 12.
March 16 – Collected one proof (either 10 or Mary’s theorem.) Finished reading/explanation of theorems in Chapter 3.
Homework: CATCH UP writing any proofs that you have not completed. Section 3.6 – 1 i, iii, v, etc and 8.
March 14 - Discussed Theorems 3.6.3, proved 3.6.4, read cor. 3.6.5 and Th 3.6.6. Homework: Prove Mary’s Theorem:
If two angles are supplementary and congruent, then each angle is a right angle. Exercise 3.6 – 6 and 10. Define
Lambert quadrilateral. Pencil in the Chapter 3 test for the 23rd.
March 4 – Discussed the Saccheri-Legendre Theorem. Began discussion of Saccheri quadrilaterals – proved 3.6.1 and
3.6.2 in class. Homework: handout – Prove Kasie’s Theorem Section 3.5 – 1. Define Saccheri quadrilateral.
March 2 – Collected the problems assigned to pairs/single students. Discussed proofs of 3.3 12 & 13. Outlined proof of
HL, then outlined proofs of corollaries of the Alternate Interior Theorem. Homework: Read the proof of the Alternate
Interior Theorem. Section 3.4 – write the proof of at least 2 from 1, 2, and 4. You are not required to read proofs of
theorems 3.4.5 through 3.4.9.
February 29 – Discussed the rest of the theorems in Section 3.3 – Homework: Complete the problem assigned to you
during class. Review 12 or 13 from Section 3.3 (be sure you have one written), Terrence’s theorem, and at least one
more from the list of 1, 3, 4, 5, or 7. Probable test date is the week of March 21.
February 26 – Discussed several theorems and outlined one proof in class. Homework: Complete previous homework
assignment. In Section 3.3 – 12 or 13. In Section 3.4 - #2. I will bring a statement of Terrence’s Theorem to class for
homework next time.
February 24 – Students helped Dr. Floyd bisect each side of a triangle. Bisectors are concurrent at the circumcenter.
Circumscribed circle was constructed. Medians were constructed to locate the centroid. Homework: Practice
constructing the circumcenter/circumscribed circle of acute scalene and right triangles. Locate the centroid of each.
Define: median of a triangle, centroid, circumcenter and exterior angle of a triangle. Prove: Diane’s Theorem –
Perpendicular lines intersect to form 4 right angles. Exercises 3.2 #9.
February 22 – Students wrote problems on the board and we critiqued them. Homework: READ section 3.2. Prove
from 3.2.1 - congruence of segments is an equivalence relation. Prove either 3.2.2 i or ii and Prove 3.2.3. Complements
of congruent angles are congruent.
February 19 – Quiz: Discussed Neutral Geometry. Began a proof that congruence of angles is an equivalence relation.
Homework: Sarah 3.2.2 i; Kasie 3.2.2.ii; Diane – Supplements of the same angle are congruent; Mary – Complements of
the same angle are congruent; Caleb – Supplements of congruent angles are congruent; Tucker – Complements of
congruent angles are congruent; Terrance – 3.2.4; Garrett – one of the above. Then everyone is to prove another of
those listed above. Define: midpoint; angle bisector; and vertical angles (Two non-adjacent angles formed with two
lines intersect.)
February 17 – Discussed non-Euclidean geometries. Homework: State the Hyperbolic Parallel Postulate and the Elliptic
Parallel Postulate. Exercises 2.7 – 1 and 4.
February 15 – Test on Chapter 1 through 2.5 – early by appointment.
February 12 – Completed reading through SMSG Axioms. Homework for February 17 – Section 2.6 - #8. . Define:
linear pair, supplementary and complementary.
February 10 – Wrote one proof. Defined several terms and began a discussion of SMSG. Homework: Define kinds of
triangles; scalene, isosceles, equilateral, acute, obtuse, right; congruent polygons and space. Exercises 2.6 – 1, 2, 3, and
5.
February 8 – Discussed Birkhoff’s Geometry. Homework: Define adjacent angles and dihedral angles. Section 2.4 – 10
Section 2.5 – 3, 4, 6 (at least two parts).
February 5 – NO Class – Science and Mathematics Tournament.
February 3 – Returned quiz. Completed reading Hilbert’s axioms. Made extensive definitions. Homework: Define:
congruent segments, congruent angles, half-plane, opposite rays, angle, interior of an angle, acute angle, obtuse angle,
right angle, perpendicular lines, polygon (know the prefixes for 3-sided polygons through 12-sided polygons), and
diagonal of a polygon. Exercises 2.4 – 2, 8, 11, 12, 13 and 16. Read section 2.5 before Monday. Test on Chapter 1
through 2.5 will be Friday the 12th.
February 1 – Returned quiz from 29th. Quiz on homework. Began the discussion of Hilbert’s Axiomatic system.
Homework: Define – radius of a circle. Exercises 2.4 – 5, 7, and 9. To clarify, Feb 10th is earliest possible test date.
January 29 - Quiz on Euclid’s Fifth Postulate. Constructed a segment bisector and an angle bisector. Defined between,
segment, ray and half-line. Homework: Be prepared to state Playfair’s Postulate. Know the definitions and symbols for
between, line segment, ray and half-line. Exercises 2.3 – 2, 3, 4, 5, 6, 9, 10. READ section 2.4 and be prepared to tell the
class how Hilbert’s Axioms are like and unlike Euclid’s Axioms . Probable test date is February 10.
January 27 – Answered some homework questions. Began discussion of Euclid’s Axiomatic Geometry. Demonstrated
two constructions. Homework: Be prepared to state Euclid’s 5th Postulate. Use Euclidean tools to construct a
perpendicular line to line l through a point P not on l and a perpendicular line to line l through a point P on l . Read
Chapter 2 through section 2.2 Exercises 2.2 - 3 a and b; 13. Earliest test date is second week of February (Sci/Math
Tournament is next week.)
January 25 – Returned graded papers from the semester. Discussed the Axioms of an Incidence Geometry, Theorems of
an Incidence Geometry, modification of Fano’s to create Young’s Geometry, and three alternatives for parallel lines
through a point to a line. Homework: Define: circle, sphere, parallel lines, skew lines, affine geometry, and projective
geometry. Exercises 1. 3, Exercises 1.4 – 1, 3 i, iii, v, vii, ix (at least) 4, 6, and 11.
January 22 – Students turned one proof of their choice. Homework: Read Section 1.4 and pay particular attention to
the incident axioms. Section 1.3 – 18 . . . catch up on homework if you need to.
January 20 – Looked at Diane’s proof of Theorem 2 from Section 1.2 – Discussed Fano’s geometry. Homework: KNOW
the axioms for the four-point geometry and Fano’s axioms. Exercises 1.3 – 4, 14, 16 (work at least two of these.)
January 15 – Collected problems due. Proofs/problems were put on the board. Discussed models for the four point
geometry. Homework: Define: collinear and noncollinear. Exercises 1.2 – 2, 25. Page 20 read the proofs of the four
theorems for the four-point geometry. Exercise1.3 – 5, 6, and 8 or 9.
January 13 – Quiz. Discussed a finite axiomatic system (Fe & Fo) and the properties of axiomatic system. Homework:
Read through page 16 at least. Exercises 1.2 – 1 & 3 (you may use #2 like you have already proved it) 16.
January 11 – Discussed the four parts of an axiomatic system (undefined terms, defined technical terms, axioms,
theorems). Assigned group problems. Homework: Know the parts of an axiomatic system. Section 1.1 - #5(due
Wednesday), and #1 – Caleb, Grace and Terrance; #2 – Garret, Tucker and Diane; #9 – Sarah and Mary; and #10 –Kasie
and Brianna. Group problem is due on Friday.