Week 1 Notes- Circles
Week 1 Notes- Circles MATH 209
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This 8 page Class Notes was uploaded by Emma Foster on Saturday January 24, 2015. The Class Notes belongs to MATH 209 at University of Alabama - Tuscaloosa taught by Katherine Nichols in Spring2015. Since its upload, it has received 322 views.
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Date Created: 01/24/15
jammy lfiDlO MATH 209 Geometry and Measurement Overview Geometry 2D and 3 D Visualization Angles Circles and Spheres Triangles Quadrilaterals and Other Polygons Constructions with Straightedge and Compass Polyhedra and Other Solid Shapes Transformations Symmetry Congruence of Two Triangles Similarity and Scale Factors Measurement Fundamentals of Measurement American Customary System and Metric System Converting From One Unit of a Measurement System to Another Measurement System The Moving and Additivity Principles about Area Areas of Triangles Parallelograms and Circles Relating the Perimeter and Area of a Shape Volumes of Prisms Cylinders Pyramids and Cones Circles and Spheres Activity You need a ruler Use a ruler to draw 5 different points that are 1 inch away from the point P When Two Circles Meet onelmiomneomcr 6 mm Ol woo poms 0 m 0w meal mm m 0m 90ml Application If you are 1 5 miles from my house you are a circle of radius 5 miles centered at my house on or muscle At least 5 miles from my house you are a circle of radiu y at my house cle T y I f 391 More than 5 miles from my house you are centered at my house 00 or midi At most 5 miles Less than 5 miles MOB West lt r East South Example Billy and Mandy live 8 miles apart Find all possible locations for their playhouse if it is A 5 miles from Billy s house and 7 miles from Mandy s house minim clam an A A A A A A A A A t A A 3347 L Billy and Mandy live 8 miles apart Find all possible locations for their playhouse if it is B 5 miles or more from Billy s house but less than 7 miles from Mandy s house 63 3 a I 4 7 r39r OCUIMH39 3 v zquot 7 yaw c u s x quotV l cm 239 WV 39 I w fl7 f a he n w p I ii 3939nir in J r 2 m L7W l 7 vw p m xx USlng Circles Example Suppose that 1 hour and 45 minutes ago a prisoner escaped from a prison located at point P shown on the map that follows Due to the terrain and the fact that no vehicles have left the area police estimate that the prisoner can go no faster than 4 miles per hour Show all places on the map where the prisoner might be at this moment 7 ml 635 W l Dl llm 4 13133quot P Example The treasure map for this exercise shows an X and an O marking two spots The treasure is described as buried treasure under a spot that is 30 feet from X and 50 feet from 0 Using this information to help you show where the treasure map might be buried iS the information enough to tell you exactly where the treasure is buried Explain l I 4 V V V v a 4 1 21 39 7714 7 l 10 feet nor among m Example 2D Trilateration Imagine you are somewhere in the United States and you are TOTALLY lost for whatever reason you have absolutely no clue where you are You find a friendly local and ask quotWhere am I He says You are 625 miles from Boise Idaho This is a nice hard fact but it is not particularly useful by itself You could be anywhere on a circle around Boise that has a radius of 625 miles like this You ask somebody else where you are and she says quotYou are 690 miles from Minneapolis Minnesota Now you re getting somewhere If you combine this information with the Boise information you have two circles that intersect You know that you must be at one of these two intersection points if you are 625 miles from Boise and 690 miles from Minneapolis If a third person tells you that you are 615 miles from Tucson Arizona you can eliminate one of the possibilities because the third circle will only intersect with one ofthese points You now know exactly where you are Denver Colorado
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