FOUNDATIONS OF
GEOMETRY
Errata (first printing)
These errors were corrected in the second printing
January 2006
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Page 7, line 13. The word "to" is missing. (Should be: "...applied to the triangle....")
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Page 19, line 31. Strike "s" from "questions". (Should be: "...a basic question regarding....")
[Reported by Kyle Engels.]
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Page 26, line 20. Add "s" to happen. (Should be: "Since this happens for every....")
[Reported by Chelsie Pitsch.]
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Page 29, line 7 of Exercise 2.1. Delete "the table". (Should be: "...lie on to mean resting on.")
[Reported by Mowaffaq Hajja]
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Page 45, line 19. Change "properties" to "property."
[Reported by Mowaffaq Hajja]
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Page 49. On line 18, change "the the" to "the;" on line 21, change "functions" to "function."
[Reported by Mowaffaq Hajja]
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Page 67, line 10. Change "the the" to "the."
[Reported by Mowaffaq Hajja]
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Page 71, 9 lines from bottom of page. Change the second f(B) - f(A) to f(B) - f(C).
(Should be: "... so f(C) - f(A) and f(B) - f(C) have the same sign....")
[Reported by Michael Salwen.]
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Page 71, first line of statement of Corollary 5.7.2. Change the second C to B. (Should be: "... three points such that B lies on ray AC.")
[Reported by John Engbers.]
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Page 78, first line of the statement of Theorem 5.7.16. Add the word "if" after "if and only". (Should be: "... if and only if ....")
[Reported by Matt Jankowski.]
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Page 114, Figure 6.24. The labels are in the wrong size and wrong font.
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Page 122, second line of Definition 6.8.6. The symbol "∠" is missing. (Should be: "∠ BCA ≅ ∠ EFD, ....")
[Reported by Amy Marsh.]
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Page 127, line 13. The symbol "Δ" is missing. (Should be: "Δ ABC ≅ Δ CDA ≅ Δ CFE, so ....")
[Reported by John Engbers.]
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Page 129, line 7. Delete "of". (Should be "...in naming the two special types....")
[Reported by Mowaffaq Hajja]
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Page 130, line 21. Add an "s" to quadrilateral. (Should be: "...what useful tools these
quadrilaterals are.")
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Page 133, Exercise 6.35, line 2. Add a comma at the end of the line. (Should be: "...if it is not
convex, it is called a dart.")
[Reported by Mowaffaq Hajja]
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Page 133, Exercise 6.35, line 3. The sentence should end with just one period. (Should be: "...if it is not convex it is called a dart.")
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Page 135, line 3. Change "remainder" to "entirety." (Should be: "For the entire chapter ....")
[Reported by Regina Visocchi.]
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Page 150, 10 lines from bottom of page. Change "circle" to "triangle." (Should be: "Move one vertex of the triangle around....")
[Reported by Mowaffaq Hajja]
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Page 154, statement of Ceva's Theorem. Change "are concurrent if and only if..." to "are concurrent (or are mutually parallel) if and only if...."
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Page 155, line 5. Add "and " after "M, ".
[Reported by Mowaffaq Hajja]
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Page 157, second line of Exercise 7.21. Delete "each of."
[Reported by Mowaffaq Hajja]
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Page 159, line 9. Add comma after S.
[Reported by Mowaffaq Hajja]
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Page 159, Exercise 7.32(b). Replace "Use Exercise 7.30(b) to prove that..." with "If the three Cevian lines are not mutually parallel, then it may be assumed that...."
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Page 160. In Exercise T7.12. Change "determine" to "determined;" in T7.13(a), add comma after
BV.
[Reported by Mowaffaq Hajja]
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Page 167, third line from bottom of page. The symbol "∠" is missing. (Should be: "∠ CC'B' is the supplement of ∠ AC'B', ....")
[Reported by Amy Marsh.]
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Page 169, line 5. Delete the period (".") before "(RAA hypothesis)."
[Reported by John Engbers.]
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Page 174, line 9. There is an extra period after the word "is." (Should be: "... that is, choose ....")
[Reported by Regina Visocchi.]
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Page 176, last symbols in statement of Theorem 8.4.9. Both primes (') should be under the arrow.
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Page 177, last symbol in statement of Theorem 8.4.12. The prime (') should be under the arrow.
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Page 187, line 3. The words "the other" should not be repeated. (Should be: "... while the other two sides ....")
[Reported by Regina Visocchi.]
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Page 192, Exercise 8.15. Change "exits" to "exists." (Should be "... there exists a rhombus ....")
[Reported by Chris Bauer.]
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Page 193, Exercise 8.21. Change "decreasing" to "strictly decreasing." (Should be: If f : (a, b) → (c, d) is strictly decreasing and onto....")
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Page 197, second line from bottom of page. Add "if".
(Should be: "... if and only if their interiors are disjoint.")
[Reported by Mowaffaq Hajja]
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Page 198, line 6. Insert "nonempty" after "each." (Should be: "...for each nonempty polygonal region....")
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Page 198, line 11. There is an extraneous comma after R1. (Should be: "If R is the union of two nonoverlapping polygonal regions R1 and R2, then ....")
[Reported by Amy Marsh.]
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Page 198, last line. Delete "E".
[Reported by Mowaffaq Hajja]
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Page 200, lines 3 & 4. Change "area of quadrilateral" to "area of a quadrilateral" etc.
[Reported by Mowaffaq Hajja]
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Page 221, Exercise 9.3. Add "and that each pair of triangles is nonoverlapping" to the statement of the exercise.
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Page 248, line 16. Add "s" to perimeter.
(Should be: "... the perimeters of polygons....")
[Reported by Mowaffaq Hajja]
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Page 248, line 20. Delete "Abu".
[Reported by Mowaffaq Hajja]
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Page 256, second line of first full paragraph. Insert "is." (Should be: "... this is a single circle....")
[Reported by Mowaffaq Hajja]
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Page 258, line 1. Delete extraneous "the" at the beginning of the line.
[Reported by Mowaffaq Hajja]
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Page 259, first line of Exercise 10.9. Add "a".
(Should be: "...an altitude of a triangle is a line ....")
[Reported by Mowaffaq Hajja]
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Page 260, line 6 of Exercise 10.28.
Change "MacLauren" to "Maclaurin."
[Reported by Mowaffaq Hajja]
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Page 269, first line of statement of Construction Problem 11.2.7. Change "such" to "such that."
[Reported by Mowaffaq Hajja]
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Page 273. On line 3, delete "segment;" on line 8 delete "bisector;" on lines 10 and 12 change
AF to
BF.
[Reported by Rita Eisele and Mowaffaq Hajja]
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Page 275, line 4. Change "polyhedra" to "polygons."
[Reported by Mowaffaq Hajja]
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Page 278, line 2. Change "are" to "area."
[Reported by Mowaffaq Hajja]
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Page 288, line 6 of Proof of Theorem 12.2.7. Change "if" to "it." (Should be: "... it follows that ....")
[Reported by Regina Visocchi.]
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Page 294, line 14. Change "rotation" to "reflection".
(Should be: "The reflection and half-turn are different in that ....")
[Reported by Mowaffaq Hajja]
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Page 300, 7 lines from bottom of page. Add "to".
(Should be: "... we move on to the proof ....")
[Reported by Mowaffaq Hajja]
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Page 301, 6 lines from bottom of page. Add "be".
(Should be: "... proof can be used ....")
[Reported by Mowaffaq Hajja]
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Page 303, line 20. Delete "we".
(Should be: "... it could be written as ....")
[Reported by Mowaffaq Hajja]
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Page 303, line 27. Delete "s" from "translations".
(Should be: "... and translation theorems.")
[Reported by Mowaffaq Hajja]
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Page 306, line 2 of footnote. Add period after "assumed".
[Reported by Mowaffaq Hajja]
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Page 318, second line from bottom of page. Delete "s" from "preserves".
(Should be: "... that inversions preserve angles ....")
[Reported by Mowaffaq Hajja]
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Page 319, line 8. Insert comma between P' and C'2.
[Reported by Mowaffaq Hajja]
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Page 319, last line. Change AP' to A'P'.
[Reported by Mowaffaq Hajja]
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Page 320, line 7. There is a left parenthesis missing from the last term in the last displayed equation of the proof.
[Reported by Aaron Brakoniecki.]
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Page 320, item 5 in summary. Add the add the assumption that t does not pass through O.
[Reported by Mowaffaq Hajja]
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Page 322, line 3. The prime in PP' should be under the arrow.
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Page 323, first line of Exercise 12.36. Add "is".
(Should be: "Suppose T is ....")
[Reported by Mowaffaq Hajja]
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Page 323, first line of Exercise 12.42. Add comma after first m.
[Reported by Mowaffaq Hajja]
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Page 347, line 8. Hyphenate "one-dimensional" and "two-dimensional."
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Page 350, third line of first full paragraph. Change "is is" to "it is."
[Reported by Mowaffaq Hajja]
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Page 353, second line from bottom. Change "further" to "farther."
[Reported by Mowaffaq Hajja]
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Page 361, line 4. Delete "in." (Should be: "... produces a negatively curved surface.")
[Reported by Mowaffaq Hajja]
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Page 362, nine lines up from bottom of page. The word "as" is missing. (Should be: "... even though it is about as useless as anything could be....")
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Page 363, line 7. Insert "to." (Should be: "... allow you to verify....")
[Reported by Mowaffaq Hajja]
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Page 370, line 26. Add the word "with." (Should be: "... in connection with the Ruler Postulate ....")
[Reported by Regina Visocchi.]
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Page 374, line 4. Strike the word "of." (Should be: "... indirect way to measure the curvature....")
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Page 392, 6 lines from bottom of page. Change "Arabic numbers" to "Arabic numerals".
[Reported by Mowaffaq Hajja]
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Page 394, line 10. Change "Postulated" to "postulated".
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Page 415, fourth line of hint for Exercise 7.8. Line over AC missing. (Should be: "Show that m must intersect AC ....")
[Reported by Matt Jankowski.]
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Page 416, second line of hint for Exercise 8.7. Replace B with B'. (Should be: "If X is on the same side of line QC as B' ....")
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Page 416, second line of hint for Exercise 9.6. The order of the vertices in the two similar triangles does not match. (Should be: "... prove that ΔAEC and ΔADB are similar ....")
[Reported by Matt Jankowski.]
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Page 418, line 1. Change "7.22" to "7.23."
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Page 419, second line of the hint for Exercise 12.1. Strike the word "either." (Should be: "... there exist two points C and C' such that ΔABC ≅ Δf(A)f(B)P and ΔABC' ≅ Δf(A)f(B)P....")
[Reported by David Bradstreet.]
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Page 419, second line of the hint for Exercise 12.10. Change "SAS" to "SSS." (Should be: "Use SSS to prove that....")
[Reported by Jim Turner.]
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Page 423, reference 48. Delete "The".
[Reported by Mowaffaq Hajja]
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Page 423, reference 60. Change "Campridge" to "Cambridge".
[Reported by Mowaffaq Hajja]
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