Geometry

1. Geometry Day 6

2. Today’s Agenda • Class Assignment • Runway Angles • Two-dimensional Figures • Polygons • Measures • Perimeter/Circumference/Area • Three-Dimensional Figures • Prisms/Pyramids • Cylinders/Cones/Spheres • Volume/Surface area • Constructions

3. Class Assignment • Runway Angles activity

4. Polygons • A polygon is a two-dimensional closed plane figure composed of line segments. • There are no curves in a polygon. • Polygons are named after the number of sides they have.

5. Common Polygons • Some common polygons are: • Triangle – 3 sides • Quadrilateral – 4 sides • Pentagon – 5 sides • Hexagon – 6 sides • Heptagon – 7 sides • Octagon – 8 sides • Nonagon – 9 sides • Decagon – 10 sides • Other polygons have names, but they can be hard to remember. Most people abbreviate them as 11-gon, 12-gon, 35-gon, etc.

6. Convexity • A polygon is convex if each of its interior angles is less than 180. • This is a convex decagon. • If one or more interiors angles is greater than 180, then the polygon is non-convex, or concave. • This is a concave octagon.

7. Regular Polygons • An equilateral polygon is one where all its sides are congruent. • An equiangular polygon is one where all its angles are congruent. • A regular polygon is one where all its sides are congruent and all its angles are congruent.

8. Perimeter and Area • Turn to page 58 in your book and study the definitions and formulas for perimeter, circumference, and area.

9. Three-Dimensional Figures • A 3-D solid composed of flat surfaces that enclose a single region of space is a polyhedron (plural: polyhedra). • Each flat surface, or face, is a polygon. • The intersection of two or more faces is a line segment called an edge. • The point where three or more edges intersect is a vertex. • Polyhedra are named after the number of faces they have: tetrahedron, hexahedron, octahedron, etc. • Polyhedra include prisms and pyramids. • A prism is has two congruent, parallel bases that are connected by parallelogram faces. • A pyramid has one polygonal base with three or more triangular faces that meet in a common vertex. • Prisms and pyramids are named after the shape of their base(s): Triangular prism, square pyramid, hexagonal prism, etc.

10. Three-Dimensional Figures • Other types of solids that aren’t polyhedron include cylinders, cones, and spheres. • A cylinder is a solid with congruent, parallel circular bases connected by a curved surface. • A cone is a is a solid with a circular base connected by a curved surface to a single vertex. • A sphere is a set of points in space that are the same distance from a given point. A sphere has no faces, edges, or vertices.

11. Three-Dimensional Figures • A polyhedron is regular if all of its faces are regular congruent polygons. There are five types of regular polyhedra, also called Platonic Solids (see p. 68). • Extra Credit: Platonic Solid nets • Review Volume and Surface Area definitions and formulas on p. 69.

12. Assignments • Review for Test 1 • Undefined Terms • Points, lines, planes • Naming, identification, etc. • Measurements • Line segments, angles • Using Algebra to solve • Area and Perimeter • Coordinate Geometry • Midpoint • Distance • Special Angle Pairs • Adjacent • Complementary • Supplementary • Vertical • Constructions?

13. Constructions • Copying a line segment • Copying an angle • Bisecting an angle • A line, ray, or line segment that bisects an angle is called an angle bisector. • Creating a perpendicular line • Through a point on the line • Through a point not on the line • Bisecting a line segment • If a line, ray, or line segment bisects a segment and is perpendicular to it, it is called a perpendicular bisector.

14. Homework #4 • Workbook, pp. 12, 14