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MATH 334, College Geometry Name Exam 1, Spring, 2015 Instructions: Construct clear and concise arguments for problems or proofs. Credit will be given for correct steps leading to an incorrect solution or proof; little credit will be given for unsupported answers or poorly constructed proofs. Correct use of notation and symbols as adopted in class is required. Accurately drawn figures must accompany arguments. In problems 1 to 3 use axioms, definitions, and theorems for incidence geometry. 1. (9 points) Interpret point to be one of A, B, C, and D, where each is a vertex of a square. Interpret line to be one of {A, B}, {B, C}, {C, D}, and {A, D}. Interpret lies on to mean “is an element of.” (a) Draw a schematic for this geometry. (b) Is this a model for incidence geometry? If so, verify the model. If not, explain why. (c) Which parallel postulate applies to this geometry? 2. (8 points) A schematic for a geometry is shown below. There are four points (indicated by letters) and one line. A B C D (a) By adding a minimum number of points and lines to the given geometry, construct a model for incidence geometry. (b) Which parallel postulate is satisfied by the model you constructed in part (a)? 3. (12 points) Prove the theorem. A model for incidence geometry that satisfies the Euclidean parallel postulate has at least four distinct points. In problems 4 to 8 use axioms, definitions, and theorems for plane geometry. 4. (8 points) Let f : ` ! R be a coordinate function, and let A, B, and C be distinct points lying on line ` such that f(A) = 5 + f(B) = �3 + f(C). (a) Find AB and BC. (b) Use the ⇤ notation to show which point is between the other two. 5. (18 points) In the French railway metric, the distance between two points lying on the same radial is given by ⌧((x1, y1), (x2, y2)) = p (x2 � x1)2 + (y2 � y1)2. A radial is any ray whose endpoint is at the origin of the coordinate plane. (a) Show that f(x, y) = x p 1 + m2 is a coordinate function for a radial in the French railway metric. (b) Use the metric to find the distance between (�1, 3) and (6, �18). (c) Find a coordinate function for the radial that contains the points (�1, 3) and (6, �18). (d) Use the coordinate function to find coordinates for the points (�4, 12) and (3, �9), lying on the same radial. (e) Use the coordinate function to find the distance between the points (�4, 12) and (3, �9). 6. (14 points) Prove that if A, B, and C are three points such that B lies on �! AC, then A ⇤ B ⇤ C if and only if AB < AC. A B C D E F 7. (16 points) In the figure above, AB ⇠= BF ⇠= CF and \BFC is a right angle. Let µ(\ABC) = 74o, µ(\CFE) = 15o, and µ(\ECF) = 135o. Find each angle and explain what theorem(s) you used to find the angle. (a) µ(\DCE) (b) µ(\ABF) (c) µ(\BAF) (d) µ(\CEF) 8. (15 points) Let AB, BC, CD, and AD be four segments where all intersections occur only at endpoints. Prove that if A, B, C, and D do not lie on line `, and ` \ AB 6= ?, then ` i ...

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- 1. MATH 334, College Geometry Name Exam 1, Spring, 2015 Instructions: Construct clear and concise arguments for problems or proofs. Credit will be given for correct steps leading to an incorrect solution or proof; little credit will be given for unsupported answers or poorly constructed proofs. Correct use of notation and symbols as adopted in class is required. Accurately drawn figures must accompany arguments. In problems 1 to 3 use axioms, definitions, and theorems for incidence geometry. 1. (9 points) Interpret point to be one of A, B, C, and D, where each is a vertex of a square. Interpret line to be one of {A, B}, {B, C}, {C, D}, and {A, D}. Interpret lies on to mean “is an element of.” (a) Draw a schematic for this geometry. (b) Is this a model for incidence geometry? If so, verify the model. If not, explain why. (c) Which parallel postulate applies to this geometry? 2. (8 points) A schematic for a geometry is shown below. There are four points (indicated by letters) and one line. A B C D (a) By adding a minimum number of points and lines to
- 2. the given geometry, construct a model for incidence geometry. (b) Which parallel postulate is satisfied by the model you constructed in part (a)? 3. (12 points) Prove the theorem. A model for incidence geometry that satisfies the Euclidean parallel postulate has at least four distinct points. In problems 4 to 8 use axioms, definitions, and theorems for plane geometry. 4. (8 points) Let f : ` ! R be a coordinate function, and let A, B, and C be distinct points lying on line ` such that f(A) = 5 + f(B) = �3 + f(C). (a) Find AB and BC. (b) Use the ⇤ notation to show which point is between the other two. 5. (18 points) In the French railway metric, the distance between two points lying on the same radial is given by ⌧((x1, y1), (x2, y2)) = p (x2 � x1)2 + (y2 � y1)2. A radial is any ray whose endpoint is at the origin of the coordinate plane. (a) Show that f(x, y) = x
- 3. p 1 + m2 is a coordinate function for a radial in the French railway metric. (b) Use the metric to find the distance between (�1, 3) and (6, �18). (c) Find a coordinate function for the radial that contains the points (�1, 3) and (6, �18). (d) Use the coordinate function to find coordinates for the points (�4, 12) and (3, �9), lying on the same radial. (e) Use the coordinate function to find the distance between the points (�4, 12) and (3, �9). 6. (14 points) Prove that if A, B, and C are three points such that B lies on �! AC, then A ⇤ B ⇤ C if and only if AB < AC. A B C D E
- 4. F 7. (16 points) In the figure above, AB ⇠= BF ⇠= CF and BFC is a right angle. Let µ(ABC) = 74o, µ(CFE) = 15o, and µ(ECF) = 135o. Find each angle and explain what theorem(s) you used to find the angle. (a) µ(DCE) (b) µ(ABF) (c) µ(BAF) (d) µ(CEF) 8. (15 points) Let AB, BC, CD, and AD be four segments where all intersections occur only at endpoints. Prove that if A, B, C, and D do not lie on line `, and ` AB 6= ?, then ` intersects exactly one of BC, CD, or AD. Assignment 2: Supply Chain Design and Implementation This assignment will help you develop an understanding about the life cycle of supply chains including the models that are aligned with it and the cost it bears. In addition, you will develop an awareness of the elements of the supply chain that should be monitored to ensure the desired results are being obtained. Scenario: You have been asked to be a guest speaker in a high school business class. Your task is to explain the basic concepts of supply chain management to a group of students. The students will take a quiz on supply chain management based on the information in your presentation. Instructions:
- 5. Develop a creative, engaging, educational handout that students can use to prepare for the quiz. Your handout should accomplish the following tasks. 1. Diagram and explain the life cycle of a supply chain. 2. Explain, and provide examples of, the models organizations use to manage forecasting, planning, and inventory. 3. Examine, and provide examples of, the costs absorbed by organizations with respect to inventory and logistics. 4. Describe how organizations use various parameters to monitor supply chain performance and provide examples. Your handout should be written in a clear, concise, and organized manner, as well as demonstrate ethical scholarship in accurate representation and attribution of sources (i.e., APA); and display accurate spelling, grammar, and punctuation. Write a 1–2-page handout in Word format. Apply APA standards to citation of sources. Use the following file naming convention: LastnameFirstInitial_M4_A2.doc. By Wednesday, February 11, 2015, deliver your assignment to the M4: Assignment 2 Dropbox. Grading Criteria: Assignment Components Proficient Max Points Diagram and explain the life cycle of a supply chain. Diagram and explanation are accurate, logical, and reflect in- depth comprehension of the supply chain life cycle. 20 Explain, and provide examples of, the models organizations use to manage forecasting, planning, and inventory. Examples provided correctly reference models used to manage forecasting, planning, and inventory. Explanation reflects a clear and accurate understanding of concepts related to supply chain management models. 24 Discuss, and provide examples of, the costs absorbed by organizations with respect to inventory and logistics.
- 6. Costs related to inventory and logistics are accurately identified and thoroughly discussed in terms of their impact on the organization. 20 Describe how organizations use various parameters to monitor supply chain performance and provide examples. Description is accurate and detailed and reflects in-depth knowledge of parameters used to monitor supply chain performance. 16 Academic Writing Write in a clear, concise, and organized manner; demonstrate ethical scholarship in appropriate and accurate representation and attribution of sources (i.e., APA); and display accurate spelling, grammar, and punctuation. Use of scholarly sources aligns with specified assignment requirements. Wrote in a clear, concise, and organized manner; demonstrated ethical scholarship in appropriate and accurate representation and attribution of sources; and displayed accurate spelling, grammar, and punctuation. Use of scholarly sources aligns with specified assignment requirements. 20 Total 100