number of times two + signs or two – signs are found in succession.” Analytic Geometry Descartes’ greatest contribution to mathematics was developing analytic geometry. The most basic definition of analytic geometry is applying algebra to geometry. Descartes established analytic geometry as “a way of visualizing algebraic formulas”. He developed the coordinate system as a “device to locate points on a plane”. The coordinate system includes two perpendicular lines. These lines are called axes. The vertical
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Geometry Notes Second Semester I. Area‚ Surface Area and Volume & Circumference Circumference is the linear distance around the outside of a circular object. • C = π • d or π • 2r. • d = diamater or (radius • 2) • r = radius II. Perimeter Perimeter is the distance around a figure. * It is found by adding the lengths of all the sides. * Finding perimeter on the coordinate plane may require the use of the distance formula: (2 x width) + (2 x height) III. Regular Polygon • A regular
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..........................................................................1-5 Units Setup ......................................................................1-5 LINE command................................................................1-8 Coordinates ......................................................................1-8 Interactive Input method
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Introduction: Generally‚ our logo is a bird‚ one of the animals that can fly around. On the top of the logo‚ there are Chinese and Canadian national flags. In this case‚ we can compare our students in Sino-Canadian Program as the bird that will fly from China to Canada for better education. On the other hand‚ from the expression of the beautiful bird‚ we can also deduce that our students must have royal quality and great ambition. Basically‚ our bird is composed of various types of geometric
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Angle is the figure formed by two rays‚ called the sides of the angle‚ sharing a common endpoint‚ called the vertex of the angle. Angles are usually presumed to be in a Euclidean plane‚ but are also defined in non-Euclidean geometry. Angle is also used to designate the measure of an angle or of a rotation. This measure is the ratio of the length of a circular arc to its radius. In the case of an angle (figure)‚ the arc is centered at the vertex and delimited by the sides. In the case of a rotation
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Christopher Lothman Geometry Distance Formula: Translation A’ (10‚ 1) B’ (2‚ 1) C’ (2‚ 7) Rule: (x‚ y) > (x 8‚ y + 4) A2C2 = sqrt(((2 (10))^2) + ((7 1)^2)) = 10 AC = sqrt(((6 (2))^2) + ((3 (3))^2)) = 10 A2C2 = AC A2B2 = sqrt(((2 (10))^2) + ((1 1)^2)) = 8 AB = sqrt(((6 (2))^2) + ((3 (3))^2)) = 8 A2B2 = AB B2C2 = sqrt(((2 (2))^2) + ((7 1)^2)) = 6 BC = sqrt(((6 6)^2) + ((3 (3))^2)) = 6 B2C2 = BC Triangle A2B2C2 = Triangle ABC by construction
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Performance Task in GEOMETRY * Computation of the surface area‚ amount and type of needed material and the volume of the package. Volume V= L x H x W = (23 cm) (4 cm) (12cm) = (276) (4) = 1 104 cm Area A= L x W = (23cm) (12cm) = 276cm Surface Area A= 2(Lh) + 2(Lw) + 2(Wh) / 2( lh + lw + wh) = 2(23*4) + 2(23*12) + 2(12*4) = 2(92) + 2(276) + 2(48)
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Tutorials Contained in Chapter 2 • • • • • • • Tutorial 2.1: Sketch Work Modes Tutorial 2.2: Simple Profiles & Constraints Tutorial 2.3: Advanced Profiles & Sketch Analysis Tutorial 2.4: Modifying Geometries & Relimitations Tutorial 2.5: Axes & Transformations Tutorial 2.6: Operations on 3D Geometries & Sketch planes Tutorial 2.7: Points & Splines Copyrighted Material Copyrighted Material Copyrighted Material 2-1 An Introduction to CATIA V5 Chapter 2: SKETCHER Copyrighted Material
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2.06 Module One Activity Student Name: **Refer to the Module Two Activity Lesson for specific directions** Step 1: Translations and SSS Identify and label three points on the coordinate plane that are a translation of the original triangle. Next‚ use the coordinates of your translation along with the distance formula to show that the two triangles are congruent by the SSS postulate. You must show all work with the distance formula and each corresponding pair of sides to
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below‚ state the translation (i) A → A’ translation (ii) B → B’ (iii) C → C’ (iv) D → D’ (v) E → E’ (b) A Point P is located at coordinates (4‚3) on a Cartesian plane. P’ is the image of P under a translation given below. State the coordinate of P’. (i) :P’ = (ii) : P’ = (iii) :P’ = (iv) : P’ = (v) :P (vi) : P’ = (c) On the graph below‚ diagram A’B’C’D’ is the image of diagram ABCD under a translation
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