Math 112b Chapter 9 Section 1 2/17/16
Math 112b Chapter 9 Section 1 2/17/16 Math 112b Sec 004
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This 5 page Class Notes was uploaded by amber weiss on Thursday February 18, 2016. The Class Notes belongs to Math 112b Sec 004 at Southern Illinois University Edwardsville taught by cheryl eames in Spring 2016. Since its upload, it has received 10 views. For similar materials see elementary mathmatics in Mathmatics at Southern Illinois University Edwardsville.
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Date Created: 02/18/16
Chapter 9 Section 1 Math 112 B 02/17/2016 Geometry: - Lines - Surfaces - Angles - Solids Based on 4 things: 1. Undefined terms: point, line, plane 2. Defined terms: definitions; might use undefined terms to define other things 3. Axioms: assume to be true without proving them 4. Theorems: things we prove using undefined terms, definitions, axioms, and other theorems that have been proved 1) What are some ral-world items that could use models for points, lines, planes? When using these items, what would you need to clarify or emphasize for students? - Points: a dot; in math, points have NO size - Lines: chalkboard rail, number lone; in math, lines extend forever in both directions - Planes: desk top, floor; in math, goes on forever in all directions 2) What does it take to fix a line? We need two points - - Collinear: if points share the same line - Example: use 3 points, - this would be collinear this would NOT be collinear, because the points do not fall on the same line 3) Are every 2 points collinear? yes 4) Are 3 points collinear? No, sometime yes if fall on same line A line segment consists of 2 points (endpoints) and all points between are collinear. A B C - B bisects line segments into 2 congruent parts 4.Write congruence statement for 2 of above. AB is congruent BC 5. What is another segment pictures above. Line AC 6. Is line AB sane as line BA? Yes, same - Segment: endpoint and all collinear points between them - Line AB = Line BA, order doesn’t matter because direction doesn’t matter - Line: goes on forever in 2 directions - Ray: point on line with all points that lie on ONE side of point A B C 7. Give 2 names for the line above, BA, CB, AC, CA, AB, BC (these have an arrow on top representing an aray) 8. Give another name for Ray AB. RAY AC (again has an arrow on top of AC) 9. Is ray AB same as Ray BA? No, they are not the same because they are going opposite directions from each other An angle is a union between 2 arrays (sides of angle) with common endpoint (vertex) A name with 1 letter: vertex name with 3 letters: vertex MUST BE in B middle C 10. Give 2 names for the angle above. <B, <ABC, <CBA - Acute angle: less than 90 degrees - Right Angle: exactly 90 degrees - Obtuse angle: more than 90 degrees - Straight angle: exactly 180 degrees - Reflex angle: greater than 180 degrees - Vertical angle: opposite angles formed by 2 intersecting lines - Complementary: 2 angles sum of 90 degrees A way to remember, think of it as weight, if you lose (less) weight, than it is a compliment someone gives you. - Supplementary: 2 angles sum is 180 degrees People take supplements for MORE of something, more than 90. - Adjacent: 2 angles vertex and common side do not overlap For the pictures of the angles, the answers are: a) Add up to 90, complementary b) Add up to 180, supplementary c) 1 3 4 <1 and <2 are vertical <3 and < 4 are vertical <3 and <1 are adjacent <2 and <4 adjacent - Parallel Lines: DO NOT INTERSECT coplanar - Perpendicular lines: intersect to create RIGHT angles - Corresponding angles: occupy same position relative to transversal and original lines )are congruent) - Transversal= line n below - Alternate exterior angles: occupy opposite sides of the transversal on exterior of original lines (they are congruent) - Alternate interior angles: occupy opposite sides of the transversal on interior of original lines (they are congruent) - Corresponding angles: a. m<1 congruent m<5 b. M<2 congruent m<6 c. M<3 congruent m<7 d. M<4 congruent m<8 - Our parallel lines are line l and line m - M<1 and m<4 = same angles - M<3 and m<2 = same angle - Alternate exterior: m<1 and m<8 because they occupy the opposite sides of transversal - Alternate interior: m<3 and m<6 ; m<4 and m<5 n 1 2 l 3 4 5 6 m 7 8 11. list angles congruent to angle 1 ______4,5,8________ 12. what type of angle pair is <2 and <3 _______vertical________ 13. “ ‘’ <6 and <3______alternate interior_________ 14. “ ‘’ <6 and <2_____corresponding____________ 15. “ ‘’ <1 and <8________alternate exterior_________ 16. if measure of <3=45 degrees, what is the measure of angle 5? M<3 and M<5 are 180 degrees because of substitution M<7 is congruent to m<3 corresponding angles M<7+m<5= 180 supplementary M<3+m<5 = 180 180-45= 135 degrees - Curve: set of points which can be connected by a single smooth, continuos motion (draw without lifting pencil) - Simple curve: curve can be drawn without lifting pencil and witout intersection itself (except maybe start/stopping point) - Closed curve: curve but has to touch back to start doesn’t have to be simple (starts and stops at same point) - Simple closed curve: starts and stops same point cannot intersect itself Classify each following curves appropriately curve may belong to more than 1 category. 17. simple: H, A, C, D, F, G 18. closed: H, E,A,C,D,F 19. simple closed: H,A,C,D,F, THE SHAPES ARE IN OUR 9.1 PACKET - Plane region: union of simple closed curve and its interior - Convex: two points in region - Nonconvex (concave): 2 points outside region - The first shape is convex cause it is connected on the incse nd - The 2 shape is a cncave because the connection outside - Circle: set of all points in a plane that are equidistant from a fixed point (center in plane) - Tangent: touch the circle at ONE point (line) - Secant: cut throught the circle (line) - Chord: stretch across the circle (segment) QUESTION: what is the longest possible chord? Diameter
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