(Current through 12/5)
Text references are to .Kay, College Geometry: a discovery approach, Addison Wesley Longman, 2002.
Other exercises are written out or indicated by some descriptive title. Recall
that written work is due on Wednesday of week following the day it is assigned.
12/5
No new written assignment
12/2(due 12/7)
Text: p. 434 #8, p 441 #1, 4, 16
11/30(due 12/7)
Text: p.433 # 5, 13
11/28(due 12/7)
Text:p.277 # 3, 5, 11, 20
11/21(due 11/30)
Text: p.248 #18 but - in my copy of the book, the first similarity is mis-stated. It should be ABE (in that order) similar to ACF (in that order). The second similarity is correct. [Oops - I never assigned this in class]
11/18(due 11/30)
Text: p. p.232 #16 p.248 # 12
11/16(due 11/30)
Text: p. 232 #5, 12, p. 248 #4, 14, 23
11/14(due 11/30)
No new written assignment
11/11(due 11/16)
No new written assignment
11/9(due 11/16)
Text: p. 219 # 15, 21 p.232 # 17
11/7(due 11/16)
Test 2 in-class No new assignment
11/4(due 11/9)
Prove: In Euclidean geometry every Saccheri quadrilateral is a rectangle.
Text: p. 221, #9 [In Euclidean geometry, parallel lines are equidistant]
11/2(due 11/9)
No new written assignment
10/31(due 11/9)
Text: p. 203 # 3, 5, 11
10/28(due 11/2)
Prove this lemma
Lemma: In neutral geometry, if (quadrilateral)UVWX is a convex quadrilateral with right angles at U and V , then UX < VW if and only if m (angle)UXW > m (angle)VWX.
Some suggestions:
For the first part (assuming UX < VW): Show there is a point P on (segment)VW with VP = UX and show that
m(angle)UXP < m(angle)UXW, m(angle)VPX > m (angle)VWX, and m(angle)VPX = m(angle)UXP [You will need angle addition, facts about Saccheri quadrilaterals, and the exterior angle theorem].
For the second part (assuming m(angle)UXW > m(angle)VWX) use contradiction and cases: Suppose that UX is not less than VW, identify the cases, and eliminate the cases – using facts about Saccheri quadrilaterals and the first part of the lemma.
10/26(due 11/2)
Text p. 190 #11, 12
10/24(due 11/2)
Text p. 190 #4, 8, 21
10/14(due 10/26)
10/12(due 10/26)Text p. 179 #10, 13
10/10(due 10/26)Text No new written assignment
Text p. 179 # 3, 4, 11
10/7(due 10/12)
Text p. 170 #6, 8
10/5(due 10/12)
10/3(due 10/12)Text p. 170 #2, 5, 13, 18
Read (for Wednesday) Section 3.6 in the text (outline notes posted on Blackboard, also).
Text p. 162 #2, 5, 17
9/30
No new written exercises
9/28(due 10/5)
Text p. 149 #6, 8, 15, 16, 20, 24
9/26 Test 1
9/23
No new written assignment - prepare for test Mon
9/21(due 9/28)
Text p125 #3, 9, 13 p. 148, 3, 14
9/19(due 9/28)
No new written assignment
Read (for Wednesday) Section 3.3 in the text (outline notes posted on Blackboard, also).
9/16(due 9/21)
Text p111 # 3, 10, 16, 18
Read (for Monday) Section 3.1 in the text (outline notes posted on Blackboard, also).
9/14(due 9/21)
Text p111 #1, 5, 8, 13
9/12(due 9/21)
Text p99 #15, 16, 19
9/9(due 9/14)
Text p99 #1, 3, 18
9/7(due 9/14)
Text p99 #5, 6, 10
Read, Print & Bring to class Friday - Activity 3
9/5(due 9/14)
Text p.87 #4, 5, 6, 16, 20
Read Section 2.5
9/2(due 9/7)
a.) Show (prove) in the taxicab plane (Cartesian plane with taxicab distance) : If points P = (x, y1), Q = (x2, y2) , and R = (x3, y3) are collinear on a line with equation y = mx + b, then Q is between P and R if and only if the number x2 is between the numbers x1 and x3 . [You need to use the definition of “between” and the taxicab distance. Remember this is an “if and only if” statement – you must prove both parts]
b.) Text p. 87 # 11,12
Reread Section 2.4 in the text (for Monday)
8/31 Write(due 9/7): In your text: p.87, #1, 2 Read, Print & Bring to class Friday - Activity 2
8/29 Write(due 9/7): In your text: p.67, #10 and p 74,#7 Read (for Wed) section 2.4 in the text
8/26 Write(due 8/31): In your text: p.32 #1, 2, 9 Read (for Monday) Section 2.3 in the text. [The material in 2.1 & 2.2 should be familiar to you]. We will not be much concerned, in this course, with the geometry of space - so Axioms I-3 and I-4, and most of I-5, will not be very important for our work.
8/24 Print, Read, Bring to class Friday: In-class activity 1
Last update 10/5/05
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