2sofsie


 * [[image:Emperical_Symmetry.gif]][[image:Breathe_Peace.gif]]Orthographics and Cubes**
 * Lessons
 * 1) Drawing 3-D shapes (usually a cube) using Isometric Dot Paper.
 * 2) Learning and understanding Orthographic Projections.
 * 3) Using and understanding Volume and Surface Area.
 * Definitions
 * 1) **Isometric Drawing-** A Horizontal line under or on top of a cube that forms a 30° angle.
 * 2) **Orthographic projections-** Using the 6 sides of the object and putting them in projection view.




 * [[image:Breathe_Peace.gif]]Polyhedron Shapes.**
 * Lessons
 * 1) Understanding //Polyhedron//
 * 2) Comprehend similarities with Lines, Points, Planes, Segments, and Angles.
 * 3) Understanding //Dihedral Angle.//
 * Definitions
 * 1) **Polyhedron-** a closed figure consists of polygons called **faces**. Where the faces touch are called the **edges**. Where the faces meet are called the **vertices/vertex**.
 * 2) **Regular Polyhedron**- all of the faces are equal and have the same number of faces meeting together.
 * 3) **Parallel Lines**- Two planes are extending in the same direction if and only if they do not bisect.
 * 4) **Lines Perpindicular to planes-** one line is vertical to a given plane at a point, if and only if it is vertical to every line in that given plane.
 * 5) **Lines Parallel to planes-** one line that isn't in the given plane is only going to be parallel to the plane is it is parallel to any line that is not in that same plane.
 * 6) **Dihedral angle-** the angle between two planes in a dihedron.
 * 7) **Measure of a Dihedral Angle-** the angle formed by two intersecting planes.


 * For games to help you out with Geometry visit these sites:**
 * http://classroom.jc-schools.net/basic/mathgeom.html
 * http://www.gamequarium.com/geometry.html
 * http://www.apples4theteacher.com/math.html


 * [[image:Breathe_Peace.gif]]Objects and Prisms!**
 * Lessons
 * 1) Understanding Prisms, oblique prisms, and right prisms.
 * 2) Study the different lateral faces of any kind of prism.
 * Definitions
 * 1) **Prism**- a solid figure in which its ends and bases are the same size and shape and happen to be parallel to eachother, and each side is a parallelogram.
 * 2) **Base-** the bottoms and tops of a figure
 * 3) **Lateral Face-** All the faces of an object that are not bases.
 * 4) **Lateral Edges-** The edges of the faces that are not the edges of bases.
 * 5) **Right Prism-** all faces are rectangular.
 * 6) **Oblique Prism-** at least one face is nonrectangluar.
 * 7) **Diagonal of a Right Rectangular Prism-** D=√ (L²+W²+H²)

http://www.cimt.plymouth.ac.uk/projects/mepres/allgcse/pr18-es.pdf**
 * To practice at the different faces, prisms, and bases try this site:

Directions:Find the distance between the given points S(5, 5, 2) and T(9, 8, 3) ST=√(x2-x1)²+(y2-y1)²+(z2-z1)² ST=√(9-5)²+(8-5)²+(3-2)² ST=√(4)²+(3)²+(1)² ST=√(16+9+1) ST=√(26)=5.1
 * [[image:Breathe_Peace.gif]]3-D Coordinate Shapes**
 * Lessons
 * 1) Classify different features of 3-D coordinate, some are the axes, coordinate planes, and axes
 * 2) Figure out problems by using the distance formula in a 3-D form.
 * Definitions
 * 1) **Right Handed System-** a 3-D coordinate system in which axes satisfy the right hand rule.
 * 2) **Octants-** one part of out eight spaces that have 3-D coordinate system that is evenly divided by the planes: -xy, -yz, and -xz.
 * 3) **Coordinate Plane-** A grid formed by multiple lines called axes, that meet at points called and origin.
 * 4) **3-D Distance Formula-** calculated distance between points (x1, y1, z1) and (x2, y2, z2) is known as this formula: D=√ (x2-x1)²+(y2-y1)²+(z2-z1)²
 * Example of the 3-D Distance Formula:

(The Right handed Coordinate System)

**Using Drawings in Perspectives**
 * Lessons
 * 1) Understanding the use of perspective drawings
 * 2) make your own perspsective drawings with these terms and rules.
 * Definitions
 * 1) **Parallel Lines-** all lines that are parallel meet at a vanishing point.
 * 2) **Parallel Lines to the Ground-** any one line that is parallel to the given line will meet at the same point.
 * 3) **Vanishing Point-** the point in which all parallel lines meet at.



**Symmetry and Parallel Polygons**
 * Lessons
 * 1) Understanding the word Polygon.
 * 2) Putting Reflectional symmetry and Rotational symmetry to use.
 * 3) Understanding //Regular Polygons,The Central Angle of a Regular polygon, axis of symmetry, and the center of a regular polygon.//
 * Defintions
 * 1) **Polygon-** a figure in which all the sides touch and non of the sides are open.
 * 2) **Sides of a Polygon-** the segments of the polygon.
 * 3) **Vertices of the Polygon-** the endpoints of the polygon.
 * 4) **Equiangular Polygon-** all of the angles of the polygon are congruent.
 * 5) **Equilateral Polygon-** all the sides of the polygon are congruent.
 * 6) **Regular Polygon-** a polygon that is both equilateral and equiangular.
 * 7) **Center of a Regular Polygon-** the equidistant vertices of the polygon.
 * 8) **Central Angle-** the sides pass through two vertices in which is where the polygons angle vertex is.
 * 9) **Reflectional Symmetry-** at least one line splits the figure into two equal pieces that can reflect upon eachother.