Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
History of trigonometry wikipedia , lookup
Multilateration wikipedia , lookup
Euler angles wikipedia , lookup
Trigonometric functions wikipedia , lookup
Line (geometry) wikipedia , lookup
Integer triangle wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Errata for Core Connections Geometry The following changes have been made to Version 5.0 of the Core Connections Geometry text for books printed after 01/2014. Changes to the Teacher Version: Problem Number and Description of Change Page Number Date 4 6/13/14 Section 1.1 includes five engaging lesson activities. 18 6/13/14 Problems 1-9 through 1-12 part (a) 27 6/13/14 Then have teams begin their work without pointing out the “Further Guidance,” which begins with problem 1-20. 53 7/8/14 a. 107 6/13/14 regular pentagon Chapter 1 Overview Updated Section 1.1 sentence. Lesson 1.1.2 Core Problems Corrected Version 1-12, not 1-11 Lesson 1.1.3 Suggested Lesson Activity Typo. 1-47. (a) Extra square in diagram. Lesson 1.3.1 Suggested Lesson Activity. regular hexagon Change equilateral pentagon and hexagon to regular. 1-111. answers 111 6/13/14 Updated answer. 1-111. (c) equilateral hexagon → regular hexagon pentagon → regular pentagon 111 4/17/14 A kite has reflection symmetry. 119 6/13/14 a. Label each shape that you have learned about so far with its geometric name. Kite incorrect in answer. 1-120. (a) Deleted. The shapes on the resource page already have names. Errata for Core Connections Geometry Page 1 of 37 Problem Number and Description of Change Page Number Date 120 6/13/14 Where would the regular hexagon from your Shape Bucket go in this Venn diagram? What about the trapezoid? Justify your reasoning. [ regular hexagon: in only the right circle; trapezoid: neither circle (Note: The trapezoid in the Shape Bucket is not isosceles.) ] 120 5/2/14 b. 1-121. (b) regular hexagon 1-123. (b) Corrected Version B Diagram missing vertex labels. A CL 1-134. (b) C 132 7/22/14 b. y = 46 and y = –20 148 6/13/14 Avaiable for download at www.cpm.org. 173 3/13/14 “That means that it must have two pairs of angles with equal measure.” 192 3/13/14 Yes, the angles marked by a and b form a straight angle, so their measures sum to 180°. 194 3/13/14 Be sure to specify any relationship between the measures of the angles (such as whether or not they are always congruent). 210 3/13/14 Since the angles in ΔAEC must add up to 180°, m∠BED must equal 0°. Typo in answer. Lesson 1.3.2B Resource Page Updated last row. 2-11. Typo in sentence. 2-27. (c) Typo in answer. 2-30. Plural angles needed. 2-47. (b) Incorrect triangle referenced in answer. Errata for Core Connections Geometry Page 2 of 37 Problem Number and Description of Change Page Number Date Corrected Version Lesson 3.2.1 Mathematical Background 335-336 7/7/14 However, a proof of AA~ is fairly straightforward. Suppose we have ΔPQR and ΔTUV with ∠P = ∠T , and ∠Q = ∠U . Use rigid motions to get P′ = T and the rays ΔP′Q′R′ where P′Q′ = TU and P′R′ = TV . Since rigid motions preserve angles, we can think of the lines Q ′R′ and UV as lines with the same corresponding angles when crossed by the transversal TU . So by the converse of the corresponding angle theorem we know that the lines Q′R′ and UV are parallel. Updated several typos. U R At this point we may dilate ΔP′Q′R′ from P′ to = U. Then since dilations ΔP′′Q′′R′′ so that Q″ preserve parallels, Q′′R′′ is parallel to UV and both contain U. Therefore Q′′R lines ′′ is identical UV TV to . Since this line intersects (which is also P′′R′′ ) at V and R″, we must have V = R″. Hence we have found a similarity transformation taking ΔPQR to ΔTUV and so, by definition, the two figures are similar. U Q V P T ⇒ Q′ V P′ = T R′ We can also prove SAS~ in essentially the same way but with even less work. Here we begin with TV . ΔPQR and ΔTUV with ∠P = ∠T , and TU PQ = PR As above, we use a rigid to get ΔP ′Q′R′ motion where P′ = T and P′Q′ = TU and P′R′ = TV . Since rigid motions preserve lengths, we also have P′Q′ = PQ and P′R′ = PR . Dilate ΔP′Q′R′ from P′ (= T) with scale factor PTU to take Q′ to = PTV ′Q′ ′R′ U and R′ to V since dilations preserve ratios of distances. This combination of a rigid motion and a dilation is a similarity transformation that takes ΔPQR to ΔTUV , so the two triangles are similar by definition. Errata for Core Connections Geometry Page 3 of 37 Problem Number and Description of Change Page Number Date 244 10/6/16 3-58. (b) Renamed second polygon as to not use same letters as first polygon. Corrected Version RIGHT ∼ ? b. I R G F A T Lesson 3.2.2 Math Notes box. S L 349 1/19/16 352 12/31/14 b: Not enough information to determine similarity. 352 12/31/14 d: Rotation, reflection, and reduced by zoom factor of 0.5 (or translation and reflection instead of rotation and reflection). 356 3/13/14 For the diagrams in problem 3-71, find the lengths of the segments listed below, if possible. 356 3/13/14 Yes, ΔPDQ ~ ΔYZX by SAS ~. 362 1/7/14 Problems 3-82, 3-83, 3-84, and 3-86 Corrected the definition of congruent. 3-69. (b) H E If there is a series of rigid transformations that maps one shape onto the other, then the two shapes are congruent. Incorrect answer. 3-69. (d) Typos in answer. 3-72. Segments, not sides. 3-73. answer Typo in triangle name. Lesson 3.2.4 Core Problems Missing problem 3-84. 3-80. 361 Deleted first sentence as it was not a mathematically correct statement. Lesson 3.2.4 Teacher Notes 362-363 11/30/14 Each pair of figures below is related by a single dilation. Solve for the indicated side lengths. Show all work. 7/7/14 Changed “Robel” to “Cori” in three places. Problem 3-86 is about Cori, not Robel. Errata for Core Connections Geometry Page 4 of 37 Problem Number and Description of Change Page Number Date Corrected Version 362 7/7/14 If you do not have access to technology, testing the proposed “SSA” similarity condition in problem 3-86 is a bit tricky using straws or linguini. One strategy is to tape a 5 cm straw horizontally on a piece of paper. Using a protractor, students can draw a ray from one endpoint on their paper so that the angle at that vertex is 49º. Students can then take a 4 cm straw and place one of its endpoints on the opposite end of the 5 cm straw of the new triangle. They can move it around on the paper, trying to place the other endpoint on the ray they have drawn. They should find that two possible triangles can be produced, one of which is not similar to Cori’s. 372 3/13/14 You now have a complete list of the three triangle similarity conditions (AA ~, SAS ~, and SSS ~) that can be used to verify that two triangles are similar. 388 12/31/14 Since the diagram does not show that lines m and n are parallel, it cannot be concluded that ∠a ≅ ∠b. Students can use a diagram where lines n and m do not look parallel to show that angles a and b are not congruent. 399 1/17/14 Updated resource page available for download at www.cpm.org. 425 2/8/15 Since the slope ratio is ≈ 437 3/13/14 Encourage students to either trace the triangle to orient it as a slope triangle or to discuss how they can visualize transforming it to identify Δy and Δx. 438 7/7/14 The prompt in problem 4-38 asks students to write a Learning Log entry about how to find Δy and Δx. In order to be sure that students have accurate explanations, it is recommended that you pull the class together in the last 2 or 3 minutes and write a class reflection with a diagram, such as one of the triangles provided in problem 4-37. Lesson 3.2.4 Technology Notes Deleted references to points that did not exist and corrected incorrect lengths. Lesson 3.2.5 intro Triangle singular, not plural. Chapter 3 Portfolio (c) Typos in answer. Lesson 3.2.1 Resource Page Updated so point of dilation could be found. 4-12. 1 5 , y ≈ 4. Typo in answer. Lesson 4.1.4 Suggested Lesson Activity 5th paragraph, it not is. Lesson 4.1.4 Closure Updated paragraph. Errata for Core Connections Geometry Page 5 of 37 Problem Number and Description of Change Page Number Date Corrected Version 441 1/6/14 In part (a), you calculated the slope ratio for 32° as 0.625. Use the “tan” button on your calculator to verify that you get approximately 0.625 when you enter 32°. Does that button give you approximately 1.600 when you enter 58°? 443 11/14/16 4-36. (c) ≈ changed to approximately. 4-40. (c) 146.8° Impossible triangle. 5 12 20° 146.8° 3 20° x 4-51. (b) an = −7.5 − 2(n − 1) = −5.5 − 2n 450 11/9/14 455 11/30/14 b: Typo in answer (–5.5 not 5.5). 4-54. (b) and (c) Answers are exact, not approximate. 4-58. (c) c: 459 5/2/14 Typo in first sentence. 4-66. (c) = 21 40 = 52.5% Is the probability that the second contestant is a girl independent of the first contestant being a girl? 475 11/30/14 1 point is represented by the upper right portion of the model. 483 9/8/14 484 1/7/14 495 1/7/15 Updated wording to be mathematically and grammatically correct. 4-90. 7 3 10 · 4 11/30/14 After 100 attempts, and Romeo finds has found the cheese 66 times. Incorrect location stated. 4-89. (a) = 17.5% 465 Updated wording in first sentence. 4-78. (c) answer 7 40 Calculate the probability of winning either the bet on the event {7, 8, 10, 11} or the bet on the event {10, 11, 12, 13, 14, 15}. Think about the set of outcomes that will allow the bettor to win either of the bets. This set of outcomes is the union of the two events. 4 38 6 − 2 = + 38 38 8 38 Typo in fraction equation. 4-105. (c) 2(0.36) + 1(0.24) + 0(0.4) = 0.96 Typo in answer. Errata for Core Connections Geometry Page 6 of 37 Problem Number and Description of Change Page Number Date 496 4/6/14 4-106. (a) and (c) Updated answers. CL 4-123. (b) answer Corrected Version a: The expected value should be 0. c: Answers vary, but the sum of the faces must be 0. For example, change either a –4 to a –3, or change a 2 to a 3. 509 7/7/14 Incorrect first bubble in flowchart. m∠CDB = m∠CEA m∠BCD = m∠ACE ΔBCD ~ ΔACE 5-8. (c) 542 3/13/14 False (it does not mention that the lines must be parallel) 548 4/28/15 Since the spins are independent, … 561 1/21/14 Write an equation for each sequence. 569 3/20/14 Decide if each pair of triangles below are similar. If they are similar, give a sequence of transformations that justifies your conclusion. If they are not similar, explain how you know. Answer had incorrect punctuation. 5-20. Typo in answer. 5-43. Updated problem prompt. 5-58. Removed “rigid” from problem prompt and updated answers. a: Not similar b: Similar: Rotate ΔGHI, translate, then dilate. c: Similar: Reflect ΔMNP, translate, then dilate. d: Similar: Rotate ΔTUV, translate, then dilate. 5-65. (b) 575 2/23/15 Answers vary. Once students solve for all the angles, they need to state that two pairs of corresponding angles have equal measure, such as m∠A = m∠D and m∠B = m∠E to reach the conclusion that ΔABC ~ ΔDEC by AA ~ or AC = AC BC and DC = EC, so DC = BC EC and m∠ACB = m∠DCE therefore ΔABC ~ ΔDEC SAS ~. 576 9/8/14 cos 38º = sin 52º Updated answer. 5-66. Typo in last answer. Errata for Core Connections Geometry Page 7 of 37 Problem Number and Description of Change Page Number Date Corrected Version 591 1/21/14 Stephen does not like yogurt very much, but he loves apples. Since both make a good snack, Stephen’s mom makes a deal with Stephen. She will keep the refrigerator stocked with 5 yogurts, 2 green apples, and 3 red apples every day. Each day, Stephen will randomly pick a snack. What is the probability Stephen will not get three yogurts on three consecutive days? Use a tree diagram or area model to show all the possible outcomes in the sample space. 600 1/21/14 Note that there is not a way to solve for the second solution other than to subtract the first solution from 180º. Students will learn in a subsequent course that sin x = # generally has two solutions for 0º ≤ x ≤ 360º by using a unit circle, but a calculator will only provide one solution. 609 1/7/15 Does this confirm the results from problem 5-118? 618 2/8/15 5-93. Switched order of last two sentences. Lesson 5.3.4 Added to first paragraph of the Suggested Lesson Activity. 5-119. Incorrect problem reference in last sentence. Chapter 5 Portfolio Part (b) number (1) triangle missing leg length. Chapter 5 Portfolio x 60° 5 619 2/8/15 The color of the bike is independent of its type. 620 7/7/14 If m∠B = 80º, m∠ACB = 29º, AB = 14, and DE = 12, find CE. 624 12/8/14 Part (b) number (3) added sentence for clarity. CL 5-140. (b) 29 degree angle was missing its degree symbol. CL 5-140. (a) answer Similar, not congruent in last bubble. ∠ACB ≅ ∠ECD ∠B ≅ ∠D ΔACB ~ ΔECD AA ~ CL 5-140. (b) answer 624 7/7/14 b. CE ≈ 24.38 “x” is not in the problem. CE, not x. Errata for Core Connections Geometry Page 8 of 37 Problem Number and Description of Change Page Number Lesson 5.3.1 Resource Page Date Corrected Version 629 10/28/14 Updated resource page available for download at www.cpm.org. 645 1/19/16 If two figures have the same shape and are the same size, they are congruent. Since the figures must have the same shape, they must be similar. 657 4/6/14 Then Mary Sue added, “Oh, then we can rotate ΔA′B′C′ about point D to get ΔA″B″C″ with A′′B′′ pointing in the same direction as DE , ... 658 2/8/15 Discuss how their previous strategy needs to be changed to show that these triangles are congruent using rigid transformations. 665 1/6/14 m∠PRQ = m∠TRS 670 3/13/14 Problem 6-45 asks students to complete a Learning Log entry about converses. 671 3/13/14 Do you think that all converses of true statements are also true? 678 1/7/15 Shortened edge length arrows to indicate length of table on the inside. 679 1/7/15 Removed diamonds from edges of table. Diagram (a) was missing side labels. Lesson 6.1.1 Math Notes box Deleted incorrect definition of congruent. 6-20. 4th paragraph: with not with the 6-20. (b) Rigid transformations, not translations. 6-31. answer Typo in angle name. Lesson 6.1.5 Closure Incorrect problem reference. 6-42. Updated question in problem prompt. 6-53. Updated diagram. 6-54. (b) Updated diagram. 6-55. (c) Also updated the resource page. 680 2/8/14 x ≈ 265.48 686 3/26/14 No special statements can be made because vertical angles are always equal. Incorrect answer. 6-62. (c) Typo in answer. Angles, not lines. Errata for Core Connections Geometry Page 9 of 37 Problem Number and Description of Change Page Number Date Corrected Version 692 1/7/15 The ball must be hit from at least ≈ 8.57 ft. Depending on where Carina stands, the ball may hit the ground at an angle of ≈ 7.5º to 8.1° with the ground. 693 12/8/14 What triangle tool can you use to find the angle of depression of the path of the ball? Find the acute angle the path of the ball makes with the ground. [ inverse tangent; ≈ 8.13° ] 702 3/26/14 If the base angles of a triangle are congruent, then it is isosceles. 710 3/26/14 x ≈ 49.94 , Triangle Angle Sum and isosceles triangle 772 2/23/15 Also, congruent triangles guarantee that m∠ADC = m∠BDC. Since m∠ADC + m∠BDC = 180º, then m∠ADC = 90º and the diagonals must be perpendicular. 774 6/20/14 Write an equation for each of the following sequences. 775 12/8/14 Similar, because if the Pythagorean Theorem is used to solve for each unknown side, then 3 pairs of corresponding sides have a common ratio; thus, the triangles are similar by SSS ~). 781 3/26/14 6-68. (a) Incorrect angle answer. 6-70. (c) Deleted reference to angle of depression. Incorrect answer. 6-86. (a) Typo in problem. Then, not the. 6-97. (d) Degrees symbol deleted from answer. 7-52. (d) Typo in answer. 7-57. Updated wording (equation not expression). 7-59. (c) Incorrect answer. 7-63. T U b “c” missing from diagram. W Lesson 7.2.3 Suggested Lesson Activity 786 3/26/14 a V As students offer statements of fact, create a list for whole-class display with each fact and reason. Last full paragraph, display, not diplay. Errata for Core Connections Geometry Page 10 of 37 Problem Number and Description of Change Page Number Date 802 1/22/14 m∠PMA = m∠PMB = 90º 810 3/26/14 ∠JEF ≅ ∠H and ∠G ≅ ∠JFE (if lines are parallel, corresponding angles are congruent). Therefore, ∠JEF ≅ ∠JFE. 827 1/7/15 Graph on ABCD if A(1, 4), B(6, 6), C(4, 1), and D(–1, –1). 834 5/2/14 Thus, if A(1, 3) and B(5, 8) , then Δx = 5 − 1 = 4 and Δy = 8 − 3 = 5 . Then the x-coordinate of M is 1+ 12 (4) = 3 and the y-coordinate is 3 + 12 (5) = 5.5 . So point M is at (3, 5.5). 848 2/1/14 Must be: none; Could be: rectangle, square, isosceles trapezoid 878 3/26/14 Later, after students use this method repeatedly in problem 8-14, students should notice that the number of triangles is always two less than the number of sides of the polygon. 878 3/20/14 Discuss problem 8-14 before moving teams on to problems 8-15 and 8-16. 881 3/26/14 Rhombus: Since a rhombus is a parallelogram, it has all of the properties of a parallelogram. In addition, its diagonals are perpendicular bisectors that bisect the angles of the rhombus; the diagonals also create four congruent triangles. 883 2/8/15 All of these are correct 7-92. Corrected Version Typo in “Statements” column of proof. 7-106. (c) Updated answer as angles E and F were ambiguous. 7-131. (a) Deleted the word “on”. Lesson 7.3.3 Math Notes box Incorrect midpoint given in example. CL 7-156. (a) Incorrect answer. Lesson 8.1.2 Suggested Lesson Activity Incorrect problem reference 4th paragraph. Lesson 8.1.2 Suggested Lesson Activity Incorrect problem reference in last paragraph. Lesson 8.1.2 Math Notes box Updated wording in “rhombus” paragraph. 8-23. (e) Incorrect phrase. Errata for Core Connections Geometry Page 11 of 37 Problem Number and Description of Change Page Number Date 884 3/20/14 They will also construct viable arguments for problems that result in no solution and write counterexamples. 906 3/21/14 A quadrilateral with diagonals that are perpendicular bisectors of each other. [ Rhombus ] 911 2/7/14 Write down any observations or patterns you found while working on problem 8-67. 919 2/23/15 His girlfriend decides to divide the cookie into 12 separate but congruent pieces. After 9 of the pieces have been eaten, what area of the cookie is left? 919 4/1/16 a150 = – 57.5 920 2/8/15 ∠ADB ≅ ∠CBD 921 5/2/14 Students will discover the area and circumference formulas for a circle with radius 1. Lesson 8.1.3 Mathematical Practices Sentence ended in a comma. 8-61. (d) Updated wording and answer. 8-68. Incorrect problem reference. 8-84. (b) Updated wording. 8-86. Corrected Version Incorrect answer. 8-87. Typo in middle bubble of flowchart. Lesson 8.3.1 Lesson Objective updated. Lesson 8.3.1 922 11/30/14 Take this opportunity to congratulate the class for discovering π. You may want to elaborate that making predictions based on data like this is one of the core concepts of calculus. Then problem 8-92 asks students to write a Learning Log entry about what they learned during this lesson. You could have the students do a Peer Edit. 926 2/23/15 6x + 18º = 2x + 30º, x = 3° 933 2/23/15 P ≈ 10.2 units Closure updated. 8-97. (b) Typo in answer. 8-106. (b) Incorrect answer for perimeter. Errata for Core Connections Geometry Page 12 of 37 Problem Number and Description of Change Page Number Date 934 9/8/14 If the length of a side of the polygon is 2 units, what is the area of the polygon? 935 7/7/14 Box with string or one string per team to simulate problem 8-114, recommended 938 5/2/14 In Lesson 8.3.2, you developed methods to find the area and circumference of a circle with radius r. 941 3/20/14 AC = BC 942 6/20/14 2.8 and –2.8 943 4/29/15 a: supplementary angles sum to 180º; x = 26º 8-107. (b) Missing the word units. Lesson 8.3.3 Materials Incorrect problem reference. Lesson 8.3.3 introduction Incorrect lesson reference. 8-118. Corrected Version Statement 4 does not need segment bars. 8-120. (c) Incorrect answer. 8-124. Typo in answer (c) and all answers missing degree symbols. 8-125. (b) b: alternate exterior angles are congruent; x = 5º c: Triangle Angle Sum Theorem; x = 15º d: exterior angle equals sum of remote interior angles; x = 35º 944 2/27/15 If the area of ΔABE is 19 cm2, what is the area of ΔACD? [ 19(4) = 76 cm2 ] 944 2/23/15 square cm in both answers 952 2/8/15 m∠C = 32º 950 4/28/15 Updated problem to correct area of triangle. 8-128. Answers need “cm” not units. CL 8-133. (d) Typo in answer. CL 8-136. (a) Impossible quadrilateral in diagram. 2x + 50º 3x + 25º x = 25º Errata for Core Connections Geometry Page 13 of 37 Problem Number and Description of Change Page Number 8-138. (e) 950 Date 10/28/15 e. Updated wording. CL 8-139. (b) Corrected Version Find the measure of an exterior angle of a regular polygon with 10 sides. 953 2/8/15 m = 50º, supplementary angles i = 51º, Triangle Angle Sum Theorem 982 12/9/14 986.16 · 16 ≈ 15,778.61 square mm 1010 4/6/14 uuur That is, find AD such that ∠BAD ≅ ∠CAD. Updated answer. 9-20. (b) Typo in answer. 9-64. (d) Typo in last sentence. ∠CAD not ΔCAD. New diagram in which AB = AC. Updated diagram. 9-73. 1015 4/29/15 Bread Incorrect tree diagram answer. Protein Condiment mayo salami white plain mayo turkey plain mayo ham plain mayo salami grain plain mayo turkey plain mayo ham 9-101. (d) plain 1038 9/8/14 How does this help explain that 1054 4/1/14 Updated resource page available for download at www.cpm.org. BP BE = 2 3 ? Last fraction had an incorrect denominator. Lesson 9.2.1 Resource Page First row of page 2 is problem 9-65 (d). Errata for Core Connections Geometry Page 14 of 37 Problem Number and Description of Change Ch. 10 Suggested Assessment Page Number Date 1073 7/8/14 Counting the number of outcomes in complex cases that require combining smaller counts of permutations and/or combinations, as in problem 10-179 and in the classwork problems of Lesson 10.3.5. 1086 7/8/14 x = 56º, y = 28º 1094 12/8/14 a. Timothy decided to create two triangles (ΔBED and ΔAEC). Typo in 2nd to last bullet. Combining, not combing. 10-16. (f) answer Corrected Version Both answers were x = . 10-27. Incorrect triangle names. AEC not ACE. 10-28. c. How are ΔBED and ΔAEC related? 1094 4/17/14 A polygon is said to be inscribed in a circle when each of its vertices touch the circle. 1096 4/29/15 = 2 p − 2k = 2( p − k) = 2m∠EAC mEC 1097 7/8/14 and a. What is the relationship between AB ? How do you know? CD Typo: its, not is. Lesson 10.1.3 Math Notes box Incorrect formula in second to last paragraph. 10-32. Updated wording in parts (a) and (b). Lesson 10.1.4 Suggested Lesson Activity or CD ? b. Which has greater measure AB Which has greater length? Explain. 1099 7/8/14 If time allows, problem 10-42 prompts students to prove that the intersection of the angle bisectors of a triangle is the center of a circle that is inscribed in the triangle (a relationship introduced in Chapter 9). 1103 7/8/14 Using the same reasoning as in part (b), ΔBPD ≅ ΔBFP because of AAS since ray BP is an angle bisector. 1112 4/29/15 In part (d) of this problem, students are introduced to the term mutually exclusive events. Incorrect problem reference in last paragraph. 10-42. (d) answer Incorrect triangles listed. Lesson 10.2.1 Suggested Lesson Activity about 10-62 Incorrect statement in sentence. Errata for Core Connections Geometry Page 15 of 37 Problem Number and Description of Change Lesson 10.2.1 Closure notes Page Number Date 1113 4/29/15 Mutually exclusive means that both events cannot occur together or at the same time (like {live on campus} and {engineering} in problem 10-64), while independent means that knowing that one event has occurred does not change the probability of the other event (like {female} and {jeans} in problem 10-63). 1127 12/8/14 Shade the cells in your table from part (b) where a student has previously taken the folder. 1130 1/7/14 m∠C = 0.5(194º) = 97º 1139 4/17/14 Thus, the heights for 175 people randomly selected people are independent of their IQs. 1140 2/8/15 • 1142 1/22/16 1142 4/11/16 Charlie’s neighbor subscribes to at least one paper. 1143 11/2/15 The Sunshine Orange Juice Company wants its product in a one-quart container (1 quart equals 57.75 cubic inches). The manufacturer for their containers makes cylindrical cans that have a base that is 5 inches in diameter. What will be the height of the one-quart container? Incorrect sentence in fourth paragraph. 10-76. (d) Incorrect part reference. 10-87. (b) Corrected Version Typo in answer – 194, not 1.94. 10-97. Repeated word. 10-100. State the Addition Rule. First bullet should be singular. 10-102. Updated art. 10-102. (c) Updated wording to be clearer. 10-103. Incorrect conversion given. Problem and answer updated. 57.75 ≈ 2.94 [ 57.75 = π(2.52)h, h = 6.25 in. ] π Errata for Core Connections Geometry Page 16 of 37 Problem Number and Description of Change 10-122. (d) Page Number Date 1156 4/29/15 How many three-number locker combinations could Carmen make up if zero could only be the second or third number and none of the numbers can be repeated? 1157 4/17/14 How is this list different from all the arrangements a child can make on a line on the refrigerator door with three magnetic letters A, B, and C? 1159 3/27/14 a: 7! = 5040 Three-number, not threedigit. 10-123. (a) First sentence below box is a question. 10-127. Typos in answers. 10-130. Corrected Version b: 1160 1/10/14 Typos in answer fractions and two-way table added. 1 5040 See two-way table at right. No, they should not charge a higher premium. 9 = 0.02586 P(ticket given red) = 348 507 = 0.02535 and P(ticket) = 20,000 . red car not red car ticket 9 no ticket 348 507 10-131. 20000 1161 1/21/14 0.64 ⋅ 0.28 ≠ 0.22 1162 4/17/14 For example, in order to calculate the home screen and enter 20. 1162 7/8/14 Prepare in advance by verifying that you know how to find permutations and combinations on the calculator models your students use. 1165 2/8/15 The number of permutations is 6 times greater than the number of combinations for the 5 choose 3 situation and 24 times greater for the 6 choose 4 situation. 1167 2/8/15 For the each of the following expressions, write down a factorial expression and then compute the value. Typo in answer. 0.64 not 0.68. Lesson 10.3.3 Materials Updated last paragraph (added 20 C 4). Lesson 10.3.3 Suggested Lesson Activity Students plural. 10-135. (a) Typos in answer. 10-141. Typos in first sentence. Errata for Core Connections Geometry 20 C4 , start from Page 17 of 37 Problem Number and Description of Change 10-141. (b) Page Number Date 1167 2/8/15 Typo in answer. 10-142. 10 P 8, not 10 P 2 10 C8 = 10 P8 8! = 10! 8!2! = 45 1168 9/8/14 Avoid the common mistake of computing P(no caffeine and no dairy) = 1 – P(coffee and dairy) because {coffee and dairy} includes all the drinks that have both coffee and dairy but does not include drinks that have only coffee or only dairy. 1175 1/21/14 Charlie and his nephew, Jake, who is a bottomless hunger pit, went to the state fair. Charlie had promised he would buy Jake three snacks. He can have one when they arrive, one midafternoon, and one when they were about to leave, or, as Jake prefers, he can have all of the snacks all at once. At the food stand the menu included seven items: Incorrect statement in last sentence of answer. 10-150. Corrected Version Updated wording. … Jake likes everything on the menu so much that he would not mind having any three items or even any two or three of the same thing. Uncle Charlie thinks variety is good so he wants Jake to choose three different things. 10-151. 1175 1/21/14 Charlie gets his way 13 of the time, so the probability that he gets his way for both “order” and “repetition” is 13 ⋅ 13 = 19 . 1188 9/8/14 13 ( 4 C3 ) ( 12 C2 ) (4)(4) = 54912 1188 2/8/15 Use a similar method for calculating the probability of getting two of a kind. 1188 2/8/15 What is the probability of getting two pairs? 1188 4/29/15 Updated answer wording. 10-172. (d) Answer should be a whole number, not a probability. 10-172. (f) Two of a kind, not one pair and then another pair. 10-172. (g) Added question. 10-172. (g) Typos in answer. Errata for Core Connections Geometry 13 C2 ⋅4 C2 ⋅4 C2 ⋅11⋅4 52 C5 = 123,552 C ≈ 0.0475 52 5 Page 18 of 37 Problem Number and Description of Change Lesson 10.3.5 Resource Page Page Number Date Corrected Version 2/8/15 Incorrect answers. 1205 and 1206 11-48. 1245 4/17/14 1248 12/31/14 Students should connect both their work with regular polygons and circles and their work with pyramids and prisms to reason out the relationship between the volume of pyramids and cones. Updated “royal flush” and “bust” answers. Updated resource page available for download at www.cpm.org. (ASA ≅) Typo in answer. ASA not AAS. Lesson 11.1.4 Suggested Lesson Activity Typo in last sentence of third paragraph. 11-99. 1278 9/8/14 Find the area of a regular decagon if the length of each side is 20 units. [ Central angle = 36°, distance from center to midpoint of side = 30.777 units, A = 12 (20)(30.777)(10) ≈ 3077.7 square units ] 1289 7/8/14 Assume that the radius of the Earth is 4000 miles. 1300 5/27/15 Number with primarily birds and under $20,000 should be 9 (not 69). 1301 9/8/14 She plans to tie three loops of ribbon about the package as shown at right. 1303 5/27/15 e: Either sum the appropriate cells: Updated problem wording and answer. 11-114. (a) Missing the word “is”. CL 11-129. Updated data to sum to 1000. CL 11-131. (b) Three, not two. CL 11-129. (e) and (f) 64+63+9+3+70+66+59+7+3+41+77+82+97 1000 Incorrect answers. = 64.1% or use the Addition Rule: 385 386 130 641 1000 + 1000 − 1000 = 1000 = 64.1% f: P(dog given < $35,000) = 64+66 64+63+9+3+70+66+59+7+3+41 = 33.7% CL 11-130. (a) 1303 4/3/14 ΔABC ~ ΔRTS (AA~) Missing parenthesis in answer. Errata for Core Connections Geometry Page 19 of 37 Problem Number and Description of Change Lesson 12.1.1 Suggested Lesson Activity Page Number Date 1328 7/8/14 Problem 12-4 gives students the opportunity for more practice in a slightly different context. 1330 7/8/14 Add a point P to your diagram and then draw a right triangle like ΔABP in the circle at right. 1336 4/3/14 In problem 12-36, teams should find a total of seven cross-sections. When they call the hyperbola a “double parabola,” correct them (hyperbolas are not made from two parabolas), and again, indicate that they will be studied in a later course. 1350 4/17/14 The farther the focus is to the directrix, the wider the parabola is and vice versa. 1353 4/3/14 Emphasize that since the distances from the points on the parabola to the directrix and to the focus are equal, then the the expressions for each of these distances can be set equal to each other. 1372 7/8/14 y-intercept: (0, 6) 1360 4/28/15 b: 1365 4/28/15 The base angles of ΔPSR must add up to 40° so that the sum of all three angles is 180°. Then add the 40° and 35° of ∠QPS and ∠QRS, respectively, and the sum of the base angles of ΔPQR must be 115°. Corrected Version Incorrect problem reference in last paragraph. 12-3. (a) Incorrect triangle referenced. Lesson 12.1.3 Suggested Lesson Activity Typo in paragraph for problem 12-36. 12-38. (c) Typo in answer. Lesson 12.1.4 Suggested Lesson Activity 3rd paragraph, last sentence, deleted the extra “the”. 12-73. (a) Incorrect y-intercept. 12-55. (b) Typo in answer. 12-61. Typos in answer. Errata for Core Connections Geometry 5 C2 ⋅4 C1 12 C3 = 40 220 ≈ 18.2% Page 20 of 37 Problem Number and Description of Change 12-66. Page Number Date 1366 4/28/15 Corrected Version 8 6 Incorrect answer. 4 2 -10 -5 5 10 -2 -4 -6 -8 12-82. (c) 1381 7/8/14 Several typos in answer. Hint: Students can start by determining the interior angles of the pentagon inside the star. The pentagon has interior angles of 108°, therefore m∠B = 108°. By drawing the bisector of ∠B, 72° AB = sin0.554° . BD = cos sin 54° . It follows that AB BD AB BD 12-85. = = 72° 0.5 + cos sin 54° + sin 54° ≈ 1.6180 = φ and 0.5 cos 72° sin 54° + sin 54° 0.5 sin 54° 0.5 sin 54° cos 72° sin 54° ≈ 1.6180 = φ . 1383 2/23/15 Thus, the y-coordinate of point C could be 2 ± 2 3 ; (5, ≈ 5.46) or (5, ≈ −1.46) . 11 4/28/15 Example 2: Calculate the area and perimeter. Typo in answer. 5.46 not 7.46. Checkpoint 4 Impossible triangle in Example 2. 9.85 cm 4 cm 5 cm 6 cm A = 12 bh = 12 ⋅ 6 ⋅ 4 = 12 cm 2 P = 6 + 5 + 9.85 = 20.85 cm Checkpoint 4 13, 14 6/1/16 10 ft 10 ft Impossible diagram in problem #7. 16 ft 8 ft 12 ft 7. Errata for Core Connections Geometry A = 144 ft2, P = 64 ft Page 21 of 37 Problem Number and Description of Change Page Number Date 27 4/28/15 Checkpoint 7 Corrected Version 4. Diagrams in problems 4 and 5 were missing the parallel marks. 15 z 4 45° 22 7 5. y 10 6 17 Checkpoint 8 31 4/29/15 a: supplementary angles sum to 180º; x = 26º b: alternate exterior angles are congruent; x = 5º c: Triangle Angle Sum Theorem; x = 15º d: exterior angle equals sum of remote interior angles; x = 35º Checkpoint 8 32 Diagrams in first three practice problems repeated CL 8-137 and had incorrect answers. 4/29/15 1. 2. 4x – 2º 3x + 2º 3. y – 48º 3y 101º 34º z Checkpoint 8 32 All work was missing degree symbols. Ex: (b) 5x + 6º = 2x + 21º 3x = 15º x = 5º Now we can go back and solve the original problems work updated. Checkpoint 8 4/29/15 32 12/21/15 10. m + 8º Impossible triangle in problem #10. 2m – 3º Errata for Core Connections Geometry m + 6º Page 22 of 37 Problem Number and Description of Change Page Number Date 33 4/28/15 congruent vertical angles, supplementary sameside interior; x = 18.5º, y = 22.5º 34 4/29/15 See errata for problem 9-73. 35 9/8/14 Checkpoint 8 All practice problem answers need the degree symbol. Answer 18 was incorrect. Checkpoint 9A Corrected Version Incorrect tree diagram answer. Checkpoint 9A Example 1 First Drink Incorrect entries in table. hot coffee Second Drink Checkpoint 9A problem 1 (b) answer hot tea hot coffee hot tea 5 8 2 8 25 64 10 64 10 64 5 8 2 8 frozen coffee slush 18 frozen coffee slush 5 8 5 64 5 64 42 9/8/14 0.09 = 9% 51 9/8/14 ≈ 172.0 ft2 55 5/27/15 V ≈ 2.362 m 3; SA ≈ 10.85 m 2 5 4/29/15 Cavalieri’s Principle Two solids have the same volume if corresponding cross-sectional areas are the same. For example, an oblique solid has the same volume as the corresponding right solid with the same height, as long as all the cross-sections parallel to the base have the same area. Incorrect answer. Checkpoint 10 problem 11 answer Incorrect answer. Checkpoint 11 problem 7 answers Incorrect answers. Glossary – Cavalieri’s Principle Parallel, not perpendicular. Errata for Core Connections Geometry Page 23 of 37 Problem Number and Description of Change Page Number Date Corrected Version 7 1/19/16 congruent Two shapes are congruent if there is a sequence of rigid transformations that carries one onto the other. The corresponding angles and sides of congruent polygons have equal measures. Congruent shapes are similar and have a scale factor of 1. The symbol for congruence is ≅. 27 1/19/16 similar figures Two shapes are similar if there is a sequence of rigid motions, followed by a dilation, that carries one onto the other. The corresponding angles of similar polygons are congruent, and the corresponding sides are proportional. The symbol for similar is ~ . See also ratio of similarity. 28 4/29/15 slope angle The acute angle a line forms with the x-axis on a coordinate graph. Also see slope triangle. Glossary – congruent New definition. Glossary – similar figures New definition. Glossary – slope angle New definition. Errata for Core Connections Geometry Page 24 of 37 Changes to the Student Version: Problem Number and Description of Change 1-47. (a) Page Number Date 28 7/8/14 a. 67 6/13/14 a. Label each shape that you have learned about so far with its geometric name. Corrected Version Extra square in diagram. 1-120. (a) Deleted. The shapes on the resource page already have names. 1-121. (b) 68 6/13/14 Where would the regular hexagon from your Shape Bucket go in this Venn diagram? What about the trapezoid? Justify your reasoning. 68 5/2/14 b. regular hexagon 1-123. (b) B Diagram missing vertex labels. C A CL 1-134. (b) 76 7/22/14 b. y = 46 and y = –20 84 3/13/14 “That means that it must have two pairs of angles with equal measure.” 94 3/13/14 Be sure to specify any relationship between the measures of the angles (such as whether or not they are always congruent). 172 10/6/16 b. Typo in answer. 2-11. Typo in sentence. 2-30. Plural angles needed. 3-58. (b) Renamed second polygon as to not use same letters as first polygon. RIGHT ∼ ? I R F A T Errata for Core Connections Geometry G H E S L Page 25 of 37 Problem Number and Description of Change Lesson 3.2.2 Math Notes box. Page Number Date Corrected Version 175 1/19/16 If there is a series of rigid transformations that maps one shape onto the other, then the two shapes are congruent. 178 3/13/14 For the diagrams in problem 3-71, find the lengths of the segments listed below, if possible. 181 9/8/14 y = −2x + 7 Corrected the definition of congruent. 3-72. Segments, not sides. 3-77. (c) Incorrect answer. 3-80. 182 11/30/14 Each pair of figures below is related by a single dilation. Solve for the indicated side lengths. Show all work. 189 3/13/14 You now have a complete list of the three triangle similarity conditions (AA ~, SAS ~, and SSS ~) that can be used to verify that two triangles are similar. 227 1/6/14 In part (a), you calculated the slope ratio for 32° as 0.625. Use the “tan” button on your calculator to verify that you get approximately 0.625 when you enter 32°. Does that button give you approximately 1.600 when you enter 58°? 229 11/14/16 Deleted first sentence as it was not a mathematically correct statement. Lesson 3.2.5 intro Triangle singular, not plural. 4-36. (c) ≈ changed to approximately. 4-40. (c) Impossible triangle. 146.8° 5 12 20° 146.8° x 4-58. (c) 239 Typo in first sentence. 4-66. (c) 243 Updated wording in first sentence. Errata for Core Connections Geometry 5/2/14 3 20° Is the probability that the second contestant is a girl independent of the first contestant being a girl? 11/30/14 After 100 attempts, and Romeo finds has found the cheese 66 times. Page 26 of 37 Problem Number and Description of Change 4-89. (a) Page Number Date Corrected Version 252 9/8/14 Calculate the probability of winning either the bet on the event {7, 8, 10, 11} or the bet on the event {10, 11, 12, 13, 14, 15}. Think about the set of outcomes that will allow the bettor to win either of the bets. This set of outcomes is the union of the two events. 253 1/7/14 272 7/7/14 Updated wording to be mathematically and grammatically correct. 4-90. 4 38 6 − 2 = + 38 38 8 38 Typo in fraction equation. CL 4-123. (b) answer Incorrect first bubble in flowchart. m∠CDB = m∠CEA m∠BCD = m∠ACE ΔBCD ~ ΔACE 5-43. 295 1/21/14 Write an equation for each sequence. 301 3/20/14 Decide if each pair of triangles below are similar. If they are similar, give a sequence of transformations that justifies your conclusion. If they are not similar, explain how you know. 315 1/21/14 Stephen does not like yogurt very much, but he loves apples. Since both make a good snack, Stephen’s mom makes a deal with Stephen. She will keep the refrigerator stocked with 5 yogurts, 2 green apples, and 3 red apples every day. Each day, Stephen will randomly pick a snack. What is the probability Stephen will not get three yogurts on three consecutive days? Use a tree diagram or area model to show all the possible outcomes in the sample space. 325 1/7/15 Does this confirm the results from problem 5-118? Updated problem prompt. 5-58. Removed “rigid” from problem prompt. 5-93. Switched order of last two sentences. 5-119. Incorrect problem reference in last sentence. Errata for Core Connections Geometry Page 27 of 37 Problem Number and Description of Change Chapter 5 Portfolio Page Number Date 332 2/8/15 Part (b) number (1) triangle missing leg length. Chapter 5 Portfolio Corrected Version x 60° 5 333 2/8/15 The color of the bike is independent of its type. 334 7/7/14 If m∠B = 80º, m∠ACB = 29º, AB = 14, and DE = 12, find CE. 338 12/8/14 Part (b) number (3) added sentence for clarity. CL 5-140. (b) 29 degree angle was missing its degree symbol. CL 5-140. (a) answer Similar, not congruent in last bubble. ∠ACB ≅ ∠ECD ∠B ≅ ∠D ΔACB ~ ΔECD AA ~ CL 5-140. (b) answer 338 7/7/14 b. CE ≈ 24.38 345 1/19/16 If two figures have the same shape and are the same size, they are congruent. Since the figures must have the same shape, they must be similar. 353 2/8/15 Discuss how their previous strategy needs to be changed to show that these triangles are congruent using rigid transformations. 361 3/13/14 Do you think that all converses of true statements are also true? 366 1/7/15 Shortened edge length arrows to indicate length of table on the inside. 367 1/7/15 Removed diamonds from edges of table. “x” is not in the problem. CE, not x. Lesson 6.1.1 Math Notes box Deleted incorrect definition of congruent. 6-20. (b) Rigid transformations, not translations. 6-42. Updated question in problem prompt. 6-53. Updated diagram. 6-54. (b) Updated diagram. Errata for Core Connections Geometry Also updated the resource page. Page 28 of 37 Problem Number and Description of Change 6-70. (c) Page Number Date 374 12/8/14 What triangle tool can you use to find the angle of depression of the path of the ball? Find the acute angle the path of the ball makes with the ground. 380 3/26/14 If the base angles of a triangle are congruent, then it is isosceles. 383 2/9/15 Deleted reference to angle of depression. 6-86. (a) Typo in problem. Then, not the. 7-1. (b) Corrected Version P Diagram missing. C 7-57. 422 6/20/14 425 3/26/14 Updated wording (equation not expression). 7-63. Write an equation for each of the following sequences. T U b “c” missing from diagram. W 7-92. a V 439 1/22/14 m∠PMA = m∠PMB = 90º 455 1/7/15 Graph on ABCD if A(1, 4), B(6, 6), C(4, 1), and D(–1, –1). 458 5/2/14 Thus, if A(1, 3) and B(5, 8) , then Δx = 5 − 1 = 4 and Δy = 8 − 3 = 5 . Then the x-coordinate of M is 1+ 12 (4) = 3 and the y-coordinate is 3 + 12 (5) = 5.5 . So point M is at (3, 5.5). 470 2/1/14 Must be: none; Could be: rectangle, square, isosceles trapezoid Typo in “Statements” column of proof. 7-131. (a) Deleted the word “on”. Lesson 7.3.3 Math Notes box Incorrect midpoint given in example. CL 7-156. (a) Incorrect answer. Errata for Core Connections Geometry Page 29 of 37 Problem Number and Description of Change Lesson 8.1.2 Math Notes box Page Number Date Corrected Version 481 3/26/14 Rhombus: Since a rhombus is a parallelogram, it has all of the properties of a parallelogram. In addition, its diagonals are perpendicular bisectors that bisect the angles of the rhombus; the diagonals also create four congruent triangles. 482 2/8/15 All of these are correct 496 3/21/14 A quadrilateral with diagonals that are perpendicular bisectors of each other. 498 2/7/14 Write down any observations or patterns you found while working on problem 8-67. 503 2/23/15 His girlfriend decides to divide the cookie into 12 separate but congruent pieces. After 9 of the pieces have been eaten, what area of the cookie is left? 504 2/8/15 ∠ADB ≅ ∠CBD 513 9/8/14 If the length of a side of the polygon is 2 units, what is the area of the polygon? 514 5/2/14 In Lesson 8.3.2, you developed methods to find the area and circumference of a circle with radius r. 517 3/20/14 AC = BC 527 2/8/15 m∠C = 32º 519 2/27/15 If the area of ΔABE is 19 cm2, what is the area of ΔACD? Updated wording in “rhombus” paragraph. 8-23. (e) Incorrect phrase. 8-61. (d) Updated wording. 8-68. Incorrect problem reference. 8-84. (b) Updated wording. 8-87. Typo in middle bubble of flowchart. 8-107. (b) Missing the word units. Lesson 8.3.3 introduction Incorrect lesson reference. 8-118. Statement 4 does not need segment bars. CL 8-133. (d) Typo in answer. 8-125. (b) Updated problem to correct area of triangle. Errata for Core Connections Geometry Page 30 of 37 Problem Number and Description of Change CL 8-136. (a) Page Number Date 525 4/28/15 Corrected Version 2x + 50º Impossible quadrilateral in diagram. 3x + 25º x = 25º 8-138. (e) 525 10/28/15 e. Updated wording. CL 8-139. (b) 528 2/8/15 553 4/6/14 Updated answer. 9-64. (d) Typo in last sentence. ∠CAD not ΔCAD. m = 50º, supplementary angles i = 51º, Triangle Angle Sum Theorem uuur That is, find AD such that ∠BAD ≅ ∠CAD. New diagram in which AB = AC. Updated diagram. 9-101. (d) Find the measure of an exterior angle of a regular polygon with 10 sides. = 567 9/8/14 How does this help explain that 593 12/8/14 a. Timothy decided to create two triangles (ΔBED and ΔAEC). BP BE 2 3 ? Last fraction had an incorrect denominator. 10-27. Incorrect triangle names. AEC not ACE. 10-28. c. How are ΔBED and ΔAEC related? 593 4/17/14 A polygon is said to be inscribed in a circle when each of its vertices touch the circle. 595 4/29/15 = 2 p − 2k = 2( p − k) = 2m∠EAC mEC 596 7/8/14 and CD ? a. What is the relationship between AB How do you know? or CD ? b. Which has greater measure, AB Typo: its, not is. Lesson 10.1.3 Math Notes box Incorrect formula in second to last paragraph. 10-32. Updated wording in parts (a) and (b). Which has greater length? Explain. 10-76. (d) 615 Incorrect part reference. Errata for Core Connections Geometry 12/8/14 Shade the cells in your table from part (b) where a student has previously taken the folder. Page 31 of 37 Problem Number and Description of Change 10-97. Page Number Date 623 4/17/14 Thus, the heights for 175 people randomly selected people are independent of their IQs. 624 2/8/15 State the Addition Rule. 625 1/22/16 625 4/11/16 Charlie’s neighbor subscribes to at least one paper. 625 11/2/15 The Sunshine Orange Juice Company wants its product in a one-quart container (1 quart equals 57.75 cubic inches). The manufacturer for their containers makes cylindrical cans that have a base that is 5 inches in diameter. What will be the height of the one-quart container? 635 4/29/15 How many three-number locker combinations could Carmen make up if zero could only be the second or third number and none of the numbers can be repeated? 636 4/17/14 How is this list different from all the arrangements a child can make on a line on the refrigerator door with three magnetic letters A, B, and C? 644 2/8/15 For the each of the following expressions, write down a factorial expression and then compute the value. Repeated word. 10-100. Corrected Version First bullet should be singular. 10-102. Updated art. 10-102. (c) Updated wording to be clearer. 10-103. Incorrect conversion given. 10-122. (d) Three-number, not three-digit. 10-123. (a) First sentence below box is a question. 10-141. Typos in first sentence. Errata for Core Connections Geometry Page 32 of 37 Problem Number and Description of Change 10-150. Page Number Date 648 1/21/14 Updated wording. Corrected Version Charlie and his nephew, Jake, who is a bottomless hunger pit, went to the state fair. Charlie had promised he would buy Jake three snacks. He can have one when they arrive, one midafternoon, and one when they were about to leave, or, as Jake prefers, he can have all of the snacks all at once. At the food stand the menu included seven items: … Jake likes everything on the menu so much that he would not mind having any three items or even any two or three of the same thing. Uncle Charlie thinks variety is good so he wants Jake to choose three different things. 10-172. (f) 657 2/8/15 Use a similar method for calculating the probability of getting two of a kind. 657 2/8/15 What is the probability of getting two pairs? 707 9/8/14 Find the area of a regular decagon if the length of each side is 20 units. 714 7/8/14 Assume that the radius of the Earth is 4000 miles. 723 5/27/15 Number with primarily birds and under $20,000 should be 9 (not 69). 724 9/8/14 She plans to tie three loops of ribbon about the package as shown at right. Two of a kind, not one pair and then another pair. 10-172. (g) Added question. 11-99. Updated problem wording. 11-114. (a) Missing the word “is”. CL 11-129. Updated data to sum to 1000. CL 11-131. (b) Three, not two. Errata for Core Connections Geometry Page 33 of 37 Problem Number and Description of Change CL 11-129. (e) and (f) Page Number Date 726 5/27/15 Corrected Version e: Either sum the appropriate cells: 64+63+9+3+70+66+59+7+3+41+77+82+97 1000 Incorrect answers. = 64.1% or use the Addition Rule: 385 386 130 641 1000 + 1000 − 1000 = 1000 = 64.1% f: P(dog given < $35,000) = 64+66 64+63+9+3+70+66+59+7+3+41 = 33.7% CL 11-130. (a) 726 4/3/14 ΔABC ~ ΔRTS (AA~) 732 7/8/14 Add a point P to your diagram and then draw a right triangle like ΔABP in the circle at right. SB: 11 4/28/15 Example 2: Calculate the area and perimeter. Missing parenthesis in answer. 12-3. (a) Incorrect triangle referenced. Checkpoint 4 Impossible triangle in Example 2. HB: 787 9.85 cm 4 cm 5 cm 6 cm A = 12 bh = 12 ⋅ 6 ⋅ 4 = 12 cm 2 P = 6 + 5 + 9.85 = 20.85 cm Checkpoint 4 Impossible diagram in problem #7. SB: 13, 14 6/1/16 10 ft 10 ft HB: 789, 790 16 ft 8 ft 12 ft 7. Errata for Core Connections Geometry A = 144 ft2, P = 64 ft Page 34 of 37 Problem Number and Description of Change Page Number Date Checkpoint 7 SB: 780 4/28/15 Diagrams in problems 4 and 5 were missing the parallel marks. HB: 803 Corrected Version 4. 15 z 4 45° 22 7 5. y 10 6 17 Checkpoint 8 SB: 793 4/29/15 HB: 806 a: supplementary angles sum to 180º; x = 26º b: alternate exterior angles are congruent; x = 5º c: Triangle Angle Sum Theorem; x = 15º d: exterior angle equals sum of remote interior angles; x = 35º Checkpoint 8 SB: 794 Diagrams in first three practice problems repeated CL 8-137 and had incorrect answers. HB: 807 4/29/15 1. 2. 4x – 2º 3x + 2º 3. y – 48º 3y 101º 34º z Checkpoint 8 SB: 794 4/29/15 Now we can go back and solve the original problems work updated. HB: 807 Checkpoint 8 SB: 795 Ex: (b) 5x + 6º = 2x + 21º 3x = 15º x = 5º 12/21/15 10. Impossible triangle in problem #10. HB: 808 All work was missing degree symbols. m + 8º 2m – 3º Errata for Core Connections Geometry m + 6º Page 35 of 37 Problem Number and Description of Change Page Number Date Corrected Version Checkpoint 8 SB: 786 4/28/15 All answers need the degree symbol. Answer 18 was incorrect. HB: 809 congruent vertical angles, supplementary same-side interior; x = 18.5º, y = 22.5º 9-73. SB: 787 4/29/15 Incorrect tree diagram answer. HB: 810 Bread Protein Condiment mayo salami plain mayo turkey white plain mayo ham plain mayo salami plain mayo turkey grain plain mayo ham Checkpoint 9A Example 1 SB: 788 plain 9/8/14 First Drink HB: 811 Incorrect entries in table. hot coffee Second Drink Checkpoint 9A problem 1 (b) answer SB: 795 9/8/14 0.09 = 9% 9/8/14 ≈ 172.0 ft2 hot tea 5 8 2 8 frozen coffee slush 18 hot coffee hot tea 5 8 2 8 25 64 10 64 10 64 frozen coffee slush 5 8 5 64 5 64 HB: 818 Incorrect answer. Checkpoint 10 problem 11 answer SB: 804 HB: 827 Incorrect answer. Errata for Core Connections Geometry Page 36 of 37 Problem Number and Description of Change Page Number Date Checkpoint 11 problem 7 answers SB: 808 5/27/15 V ≈ 2.362 m 3; SA ≈ 10.85 m 2 4/29/15 Cavalieri’s Principle Two solids have the same volume if corresponding cross-sectional areas are the same. For example, an oblique solid has the same volume as the corresponding right solid with the same height, as long as all the cross-sections parallel to the base have the same area. 1/19/16 congruent Two shapes are congruent if there is a sequence of rigid transformations that carries one onto the other. The corresponding angles and sides of congruent polygons have equal measures. Congruent shapes are similar and have a scale factor of 1. The symbol for congruence is ≅. 1/19/16 similar figures Two shapes are similar if there is a sequence of rigid motions, followed by a dilation, that carries one onto the other. The corresponding angles of similar polygons are congruent, and the corresponding sides are proportional. The symbol for similar is ~ . See also ratio of similarity. 4/29/15 slope angle The acute angle a line forms with the x-axis on a coordinate graph. Also see slope triangle. Corrected Version HB: 831 Incorrect answers. Glossary – Cavalieri’s Principle SB: 813 HB: 837 Parallel, not perpendicular. Glossary – congruent SB: 815 New definition. HB: 839 Glossary – similar figures SB: 837 HB: 861 New definition. Glossary – slope angle SB: 838 New definition. HB: 862 Errata for Core Connections Geometry Page 37 of 37