2herkou

__**6.1-Solid Shapes**__ **⁵**


 * objectives:**
 * 1) Use isometric dot paper to draw three-dimensional shapes composed of cubes.
 * 2) Develop an understanding of orthographic projections.
 * 3) Develop a basic understanding of volume and surface area.


 * Isometric Drawing: When horizontal lines of the object that are showed by lines form 30° angles.**[[image:255237607_5afd5c0acd_m.jpg align="right" link="http://www.flickr.com/photos/watz/255237607/"]]
 * Some things that will help you to better understand solid shapes is by having some isometric dot paper. This paper has diagonal rows of dots that make 30°.
 * Connect the dots to make a cube, as shown to the right. You will only see 3 faces of the cube shown most of the time.
 * Isometric dot paper can help you in many ways throughout this whole chapter. The isometric dot paper will help a lot with orthographic projections also.

Here is a site that will better your understanding of orthographic projection if you still need help. [|Click Here] This is the back, rear view. ---This is the front view.- Below is the top view. //The pricture above is by Privettandrew.- The pricture above is by Privettandrew. The pricture above is by Privettandrew.//
 * Orthographic Projection: A view of an object that in which the different sides of the object are "projected" onto a plane.**
 * Orthographic projections always have six views of itself on a plane: front, top, bottom, left, right and back.
 * Note that edges cannot be seen in some views, they are represented in dashed lines.
 * What could help you with this project is by having your own small cubes to simulate the problem.


 * __6.2-Spatial relationships__**

Faces: The flat parts of the polyhedron. Edges: The intersections of the faces. Vertices: The vertices of the faces.**
 * Objectives:**
 * 1) **Define polyhedron.**
 * 2) **Identify the relationships among points, lines, segments, planes, and angles in three-dimensional space.**
 * 3) **Define dihedral angle.**
 * Polyhedron: A closed spatial figure composed of a bunch of polygons.

A line perpendicular to a plane: A line is perpendicular to a plane at a point F if and only if it is perpendicular to every line in the plane that A line parallel to a plane: A line that is not contained in a given plane is parallel to the plane if and only if it is parallel to.**
 * Parallel Planes: Two planes are parallel if and only if they do not intersect.


 * Dihedral angle: A figure formed by two half-planes with a common edge.**


 * 6.3-Prisms

Base- The faces formed by the polygonal region. Lateral faces- the remaining faces, or quadrilaterals. Lateral edges- the edges of the lateral faces. Right prisms- all of the lateral faces are rectangels. Oblique prisms- if its not a right prism, then its oblique. Diagonal of a Right Rectangular Prism.** d = √ l² +w² + h²
 * inside a right rectangular prism with the demensions //l x w x h,// the length of the diagonal is given by


 * 6.4- Coordinate in Three Dimensions**

Distance Formula in Three Dimensions- ...**
 * Right-haded system- have your right hand shaped like a gun, and your middle finger facing left. Your index finger represents the x-axis, your thumb represents the z-axis, and your middle-figner represents the y-axis.
 * D = √ (**x2 - x1)² + (y2 - y1)² + (z2 - z1)²**


 * 6.6.- Perspective Drawing

Vanishing point: the point where parallel lines seem to meet from your perspective.** For example, have you ever looked down the rails of a railroad track, or the bars of highways? As you move further away, while looking straight down the path between two parallel objects, they seem to meet at a certain point.
 * Sets of Parallel Lines (Theorem): In a perpsective drawing, all lines that are parallel to each other meet at the vanishing point.

Lines Parallel to the Grounds (Theorem): In some pictures, a line that is in the plane in the ground in the drawing, that is not parallel to the picture plane will show at the horizon of the drawing. Any line that is parallel to this line will show at the horizon of the picture.**