1. Types of Reasoning * Inductive Reasoning – * general conclusion based on a limited collection of specific observations * educated guesses * Primary flaw – we cannot be sure the conclusion is always correct * Counterexamples -- show a conclusion reached through inductive reasoning is not true * Deductive Reasoning – * making a specific conclusion based on a collection of generally accepted assumptions. * There are no counterexamples
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Alexander Zouev 000051 - 060 - 3 - Extended Essay – Mathematics Alhazen’s Billiard Problem Introduction: Regarded as one of the classic problems from two dimensional geometry‚ Alhazen’s Billiard Problem has a truly rich history. The problem is believed to have been first introduced by Greek astronomer Ptolemy back in 150 AD1 and then eventually noticed by 17th century Arabic mathematician Abu Ali al Hassan ibn Alhaitham (whose name was later Latinized into Alhazen)2 . Alhazen
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WT + 15 = 20 WT = 5 6-6 Trapezoids and Kites Find each measure. 1. ANSWER: 5 COORDINATE GEOMETRY Quadrilateral ABCD has vertices A (–4‚ –1)‚ B(–2‚ 3)‚ C(3‚ 3)‚ and D(5‚ –1). 3. Verify that ABCD is a trapezoid. SOLUTION: First graph the points on a coordinate grid and draw the trapezoid. SOLUTION: The trapezoid ABCD is an isosceles trapezoid. So‚ each pair of base angles is congruent. Therefore‚ ANSWER: 101 2. WT‚ if ZX = 20 and TY = 15 SOLUTION: The trapezoid WXYZ is an isosceles trapezoid
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Kuta Software - Infinite Geometry Name___________________________________ Arcs and Central Angles Date________________ Period____ Name the arc made by the given angle. 2) ∠1 1) ∠FQE I F H 1 Q J E D Name the central angle of the given arc. 3) ML 4) ML L L M K 1 Q M K If an angle is given‚ name the arc it makes. If an arc is given‚ name its central angle. 6) Major arc for ∠1 5) RS B T C Q 2 1 3 S R A 7) ∠KQL
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MATHEMATICS CURRICULUM FOR SECONDARY COURSE RATIONALE Mathematics is an important discipline of learning at the secondary stage. It helps the learners in acquiring decision- making ability through its applications to real life both in familiar and unfamiliar situations. It predominately contributes to the development of precision‚ rational and analytical thinking‚ reasoning and scientific temper. One of the basic aims of teaching Mathematics at the Secondary stage is to inculcate the skill
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Reaction Paper Ric Michael P. De Vera IV- Rizal Mr. Norie Sabayan I. A and B Arabic mathematics: forgotten brilliance? Indian mathematics reached Baghdād‚ a major early center of Islam‚ about ad 800. Supported by the ruling caliphs and wealthy individuals‚ translators in Baghdād produced Arabic versions of Greek and Indian mathematical works. The need for translations was stimulated by
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Among these were Hippocrates of Chios‚ Theudius‚ Theaetetus‚ and Eudoxus. Euclid ’s vital contribution was to gather‚ compile‚ organize‚ and rework the mathematical concepts of his predecessors into a consistent whole‚ later to become known as Euclidean geometry. Euclidean constructions are the shapes and figures that can be produced solely by a compass and an unmarked straightedge. Although these tools were indeed simple‚ their range of abilities seemed unlimited. Not only could they produce a multitude
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the future? These are a few of the many questions that one asks when they have to take an algebra course. This is a required subject in most colleges to further ones education. The first year of algebra is a prerequisite for all higher-level math: geometry‚ algebra II‚ trigonometry‚ and calculus. It is quite true‚ while many people get by without an education in algebra‚ whenever they pick up the phone‚ manage their money‚ travel to some other place‚ they are unintentionally using math. Algebraic
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ABC’S OF GEOMETRY | By Parker Davis | January 2‚ 2012 | AA similarity | when two triangles have corresponding angles that are congruent as shown below‚ the triangles are similar | | AAS | if two angles and the non-included side one triangle are congruent to two angles and the non-included angle of another triangle‚ then these two triangles are congruent | | Acute angle | an angle with an angle measure less than 90° | | Acute triangle | a triangle where all three internal angles are acute
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Solids Content Area: Math Grade Level: Kindergarten Time Frame: 45 min Prior to this lesson the students had a lesson on attributes. The children defined and identified attributes in different two-dimensional shapes. MA Framework Standard: Geometry K.G Identify and describe shapes (squares‚ circles‚ triangles‚ rectangles‚ hexagons‚ cubes‚ cones‚ cylinders‚ and spheres). 2. Correctly name shapes regardless of their orientations or overall size. Identify shapes as two-dimensional (lying
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