Introduction to Geometry links & errata

Below are some of the links that are referenced in the book Introduction to Geometry. (Note: Art of Problem Solving is not responsible for the content on any external site.)

Chapter 3

Chapter 6

Chapter 9

Unfortunately, the book is not perfect. Here is a list of the known errors. If you know of an error not on this list, we would appreciate a short email to books@artofproblemsolving.com describing the error.

First Edition Text:

• Chapter 2, page 23. A little less than 1/3 down the page, "Since LPO is a line" should be "Since LPN is a line".
• Chapter 3, page 58, Exercise 3.3.1. Triangle DEF simply doesn't exist, because DF.
• Chapter 3, page 68. The first sentence in the solution to Problem 3.17 should begin, "Since DC=DB".
• Chapter 6, page 161. Problem 6.5.1(c) should be 12, 35, 37.
• Chapter 7, page 205. Problem 7.52. The equation "KL = 40" should be "KL = 30".
• Chapter 8, page 238. The area of a rhombus equals its base times its height, not half the product of its base and height (corrected in the second edition).
• Chapter 15, Problem 15.18. The problem should specify that the cube has edge length 1.
• Chapter 16, Problem 16.43. The "y-axis" should be replaced with "x-axis".

First Edition Solutions:

• Chapter 3, page 19. Problem 3.37(b): DEF need not be equilateral. It is possible to change the location of D, but not E and F, and still satisfy the conditions of the problem. Specifically, the condition that AD = CF merely forces D to be on the circle with center A and radius CF. The condition AE = CD forces D to be on the circle with center C and radius AE. There are two intersections of these circles; one of these is shown in the text. If we let the other intersection point of the circles instead be D, then all of the conditions of part (b) are satisfied, but DEF is not equilateral.
• Chapter 5, page 37. Problem 5.37: The equation in the third sentence should be AD = (AE)(BD)/EC, not AD = (AE)(BC)/EC.
• Chapter 6, page 54. Problem 6.41: 22+120+122 = 264, not 164.
• Chapter 6, page 59. Problem 6.59: In all three parts, the "16" in the boxed answers should be changed to "12".
• Chapter 7, page 193. Problem 7.5.2. Triangle XYZ in the diagram should be obtuse, with the obtuse angle at Y, and with point A on the extension of ZY past Y.
• Chapter 7, Problem 7.52: Please see the correction made to the second edition below (under "Second Edition Solutions")
• Chapter 14, page 149. Problem 14.43: There's a subtle error in the volume computation for wedge B. The piece cut off is not similar to the original wedge; a cross-section of the piece perpendicular to the "bottom" of the wedge is similar to a corresponding cross-section of wedge B. The areas of these cross-sections have ratio (1/4)^2 = 1/16. The heights between parallel faces in the direction of these cross-sections is the same in both the piece and the original wedge, so the volume of the piece is 1/16 that of the original wedge. Therefore, the remaining piecehas volume 15/16 of the original wedge. So, the desired ratio is (7/8)/(15/16) = 14/15.
• Chapter 17, page 181. Problem 17.11 asks for angle XYZ. The solution finds angle Z. The correct answer then is the complement of the boxed angle, so the answer is 60 degrees.

Second Edition Text:

• Chapter 2, page 23. A little less than 1/3 down the page, "Since LPO is a line" should be "Since LPN is a line".
• Chapter 3, page 58, Exercise 3.3.1. Triangle DEF simply doesn't exist, because <E cannot be greater than <F if DE > DF.
• Chapter 3, page 68. The first sentence in the solution to Problem 3.17 should begin, "Since DC=DB".
• Chapter 6, page 160. Problem 6.5.1(c) should be 12, 35, 37.
• Chapter 7, page 192. Problem 7.5.2. Triangle XYZ in the diagram should be obtuse, with the obtuse angle at Y, and with point A on the extension of ZY past Y.
• Chapter 15, Problem 15.18. The problem should specify that the cube has edge length 1.
• Chapter 18, Problem 18.12, page 489: In the paragraph below the "Important" box, the equation "BO=1/2" should be "OP = 1/2".

Second Edition Solutions:

• Chapter 3, page 19. Problem 3.37(b): DEF need not be equilateral. It is possible to change the location of D, but not E and F, and still satisfy the conditions of the problem. Specifically, the condition that AD = CF merely forces D to be on the circle with center A and radius CF. The condition AE = CD forces D to be on the circle with center C and radius AE. There are two intersections of these circles; one of these is shown in the text. If we let the other intersection point of the circles instead be D, then all of the conditions of part (b) are satisfied, but DEF is not equilateral.
• Chapter 5, page 37. Problem 5.37: The equation in the third sentence should be AD = (AE)(BD)/EC, not AD = (AE)(BC)/EC.
• Chapter 6, page 59. Problem 6.59: In all three parts, the "16" in the boxed answers should be changed to "12".
• Chapter 7, page 70. Problem 7.52: Part (a) should say, "KM = KL/2 = 15" and "JM = 20". The final answer is still (KL)(JM)/2 = 300. Part (b) should say "its semiperimeter is (25+25+30)/2 = 40, the inradius is 300/40 =15/2". Part (c) should say, "OM = JM - JO = 20-x", "x^2 = (20-x)^2 +15^2", and "40x = 400+225, so x = 125/8".
• Chapter 14, page 149. Problem 14.43: There's a subtle error in the volume computation for wedge B. The piece cut off is not similar to the original wedge; a cross-section of the piece perpendicular to the "bottom" of the wedge is similar to a corresponding cross-section of wedge B. The areas of these cross-sections have ratio (1/4)^2 = 1/16. The heights between parallel faces in the direction of these cross-sections is the same in both the piece and the original wedge, so the volume of the piece is 1/16 that of the original wedge. Therefore, the remaining piece has volume 15/16 of the original wedge. So, the desired ratio is (7/8)/(15/16) = 14/15.
• Chapter 17, page 190. In the solution to Problem 17.27, the equation in the box should be 2x + 5y = 0.
• Chapter 19 Solutions, page 219. Problem 19.11 asks for angle XYZ. The solution finds angle Z. The correct answer then is the complement of the boxed angle, so the answer is 60 degrees.