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Geometry warm up B E F 30° 45° 60° 45° A D C Name a ray that bisects AC or Name the perpendicular bisector of AC or Name the bisector of <CDB or When you get done with this, please make a new note book DBBD DF D is the midpoint of AC

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3.1 Symmetry in Polygons What is symmetry? There are two types were concerned with: Rotational and Reflective If a figure has ROTATIONAL symmetry, then you can rotate it about a center and it will match itself (dont consider 0° or 360°) If a figure has REFLECTIONAL symmetry, it will reflect across an axis. What are polygons? A plane figure formed by 3 or more segments Has straight sides Sides intersect at vertices Only 2 sides intersect at any vertex It is a closed figure

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Names of polygons Polygons are named by the number of sides they have: PolygonSides Triangle3 Quadrilateral4 Pentagon5 Hexagon6 Heptagon7 Octagon8 Nonagon9 Decagon10 11-gon11 Dodecagon12 13-gon13 N-gonn

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Equiangular – All angles are congruent Equilateral – All sides are congruent Regular (polygon) – All angles have the same measure AND all sides are congruent Reflectional Symmetry – A figure can be cut in half and reflected across an axis of symmetry. Rotational Symmetry – A figure has rotational symmetry iff it has at least one rotational image (not 0° or 360°) that coincides with the original image. Vocabulary

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center Central angle C A little more vocab EQUILATERAL triangle has 3 congruent sides ISOCELES triangle has at least 2 congruent sides SCALENE triangle has 0 congruent sides Center – in a regular polygon, this is the point equidistant from all vertices Central Angle – An angle whose vertex is the center of the polygon

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Activities 3.1 Activities 1- 2 (hand out) Turn it in with your homework

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What you should have learned about Reflectional symmetry in regular polygons When the number of sides is even, the axis of symmetry goes through 2 vertices When the number of sides is odd, the axis of symmetry goes through one vertex and is a perpendicular bisector on the opposite side

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What you should have learned about rotational symmetry To find the measure of the central angle, theta, θ, of a regular polygon, divide 360° by the number of sides. 360/n = theta To find the measure of theta in other shapes, ask: when I rotate the shape, how many times does it land on top of the original? Something with 180° symmetry would have 2-fold rotational symmetry Something with 90 degree rotational symmetry would be 4-fold

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Homework Practice 3.1 A, B & C worksheets

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CHAPTER 1: Tools of Geometry

CHAPTER 1: Tools of Geometry

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