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4-6 Unions and Basic Geometric Shapes Objectives: 1. draw and identify basic figures of geometry and polygons 2. identify statements as sometimes, always, or never 3. apply definition of polygon to various figures Big Idea: Some unions of rays are angles; some unions of segments are polygons. Draw a union of two rays that is not an angle. Draw the union of 3 segments that is not a triangle. Draw the union of 4 segments that is not a quadrilateral. Angle – union of two rays with the same endpoint. Named EHR, RHE, or H Sides of angle – rays that make up the angle HE and HR Vertex of angle – common endpoint of two rays. Math History – Ancient Babylonians told us that a full circle is 360 based on the fact that stars move a full circle in 365 days (1 year) but 365 not as easy to work with as 360. Protractor – instrument used to measure angles Baseline – line segment from 0 to 180. Acute angle – measures 0 x < 90 Right angle – x = 90 Obtuse angle – measures 90 < x < 180 Straight angle – x = 180 Collinear – 3 points that lie on the same line. no Polygon – a union of segments in which each segment intersects exactly two others, one at each of its endpoints. Encloses a single region in a plane yes no no Polygons have a fixed number of sides and # of sides = # of angles 3 sides = triangle 7 sides = heptagon 4 sides = 8 sides = octagon quadrilateral 9 sides = nonagon 5 sides = pentagon 10 sides = decagon 6 sides = hexagon n sides = n-gon To name a figure, start at any vertex and name all letters clockwise or counter-clockwise until back to the starting letter. Triangle is the only one with a symbol in the front. Classify – give type of polygon Name – give specific name of that polygon. (using letters)