1. 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

2. 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

3. 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

4. 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

5. 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

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

7. 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

8. 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

9. Homework Practice 3.1 A, B & C worksheets