MAT1236 Lecture Notes - Lecture 6: Euclidean Geometry, Solid Geometry, Platonic Solid
4 Jun 2018
School
Department
Course
Professor
WEEK$6$
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Geometry$
• Plane&geometry&(2D)&
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o A5/-23+56/01+-2=(593;9:01+-=(5+0/01+-(/-.(05/-2;/01+-((
• Solid&geometry&(3D)&
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Polygons$
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Regular$polygons$
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Classifying$quadrilaterals(
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Convex$and$Concave,$$
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4+;7<+-2(/59(concave(13(+-9(+5(6+59(1-095-/;(/-<;92(/59(593;9K(/-<;92((
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Area&of&parrallelogram:&F/29(K(?95?9-.1:,;/5(891<80((
Area&of&triangle:($M%(F/29(K(?95?9-.1:,;/5(891<80(
Area&of&trapezoid:($M%G/SFJK8(
Area&of&a&circle(12(?1(K(52>,/59.(
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Circles$
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.1/69095(12(089(.120/-:9(085+,<8(089(:9-059(/:5+22(089(E1.920(?/50(+3(089(:15:;9=(089(5/.1,2(12(
089(.120/-:9(F90E99-(089(:9-059(/-.(/(?+1-0(-(089(:15:,63959-:9D((
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Transformations$
U Reflections:(/:819B9.(F7(3;1??1-<(089(+FO9:0(,21-<(/(6155+5(;1-9=(089(6155+5(;1-9(12(/(
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U 05/-2;/01+-(/59(/:819B9.(F7(2;1.1-<(089(+FO9:0(/(<1B9-(.120/-:9(1-(/(<1B9-(.159:01+-((
U Dilations:(6/7(910895(F9(9-;/5<969-02(+5(59.,:01+-2=(35+6(089(:9-059(+3(
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Document Summary
Are simple closed figures with three or more straight sides, polygons are named based on the number of sides that they have. ( gon" means angle) hexagon equals 6 angles. Plane figures that are not polygons include circles and ovals, complex figures, open serves and shapes with rounded corners/curved sides. (doesn"t cross over itself) Are regular is all side lengths and angles are equal. Polygons are irregular if not all side lengths or angles are equal. May be classified according to the side lengths (all equal, opposites equal, adjacent equal), parallel side, angle size, line and rotational symmetry, length of diagonals and angle between the, convex or concave. Polygons are convex if all internal angles are less than 180 . Polygons are concave if one or more internal angles are reflex angles. Area of triangle: 1/2 base x perpendicular height. Area of a circle is pi x rsquared.
