2buremi

= = = = =Emilie's Chapter of Solid Shapes=

-Section 1
 * Objectives**
 * Use isometric dot paper to draw 3-D shapes made up of cubes.
 * Make sure you have an understanding of orthrographic projection.
 * Make sure you have a basic understanding of volume and surface area.


 * Definitions**
 * __[|Isometric Drawing:]__ An isometric drawing is a drawing where the horizontal lines of an object are 30° angles with a horizontal line in the picture.


 * __[|Orthographic Projection:]__ An orthrographic projection is a vew of an object where the points of the object are "projected" onto the picture plane along lines perpendicular to the picture plane.

-Section 2

**Objectives**

 * Define the term polyhedron.
 * Identify how points, lines, segments, planes, and angles relate to each other in 3-D space.
 * Define the term dihedral angle.


 * Definitions**
 * __[|Polyhedron:]__ A polyhedron is a closed figure with a lot of space made up of polygons that are called the faces of the polyhedron. The intersections of those faces are what is called the edges of the polyhedron. The vertices of the faces are also the vertices of the polyhedron.
 * __[|Parallel Planes:]__ The **only** time two parallel planes are parallel are if they never intersect
 * __[|A Line Perpendicular to a Plane:]__ The **only** time a line is perpendicular to a plane at a given point is if it is parallel to a line in the plane.
 * __[|A Line Parallel to a Plane:]__ The **only** time a line that isnt in a given plane is parallel to the plane is if it is parallel to a line that is in the plane.
 * __[|Dihedral Angle:]__ A dihedral angle is the figure made up by two half-planes that share an edge. Each one of the half-planes is called a face of the angle, and the shared edge of the half-planes is called the edge of the angle.
 * __[|Measure of a Dihedral Angle:]__ The measure of a dihedral angle is the measure of an angle that is made by two rays that are on the faces and that are also perpendicular to the edge.

-Section 3
 * [[image:waterfull.jpg width="391" height="272" link="http://www.flickr.com/photos/genista/8729331/"]]

Objectives**
 * Define the terms prism, right prism, and oblique prise.
 * Examine the different shapes of lateral faces of prisms.
 * Solve different problems by using the diagonal measure of a right prism.


 * Definitions**
 * __Prism:__ A prism is a polyhedron that includes a polygonal region and its reflected image on a parallel plane, with quadrilateral faces connecting its corresponding edges.
 * __Base:__ A base is the faces that are formed by the polygonal region and its image.
 * __Lateral Faces:__ A lateral face are the remaining faces, which are quadrilaterals.
 * __Lateral Edges:__ A lateral edge are the edges of the lateral face that are not edges of either base.
 * __Right Prism:__ A right prism is a prism where all of the lateral faces are rectangles.
 * __Oblique Prism:__ An oblique prism is a prism that has at least one nonrectangular lateral face.
 * __Diagonal of a Right Rectangular Prism:__ In a right rectangular prism with the dimensions of //l// x //w// x //h//, the length of a diagonal is given by: d= the square root of //l²// x //w²// x //h²//

-Section 4
 * Objectives**
 * Identify the features of a 3-D coordinate system, including the axes, octants, and coordinate planes.
 * Solve a variety of problems by using the distance formula in 3-D

//d//= the square root of (x2 - x1)² + (y2 - y1)² + (z2 - z1)².
 * Definitions**
 * __Right-handed system:__ A right-handed system is the setup of the axes
 * __Distance Formula in 3-D:__ The distance, represented by //d//, between points x1, y1, z1, and x2, y2,z2 is given by the equation

-Section 6


 * Objectives**
 * Identify and define the simple concepts of perspective drawing.
 * Apply these simple concepts to create your very own perspective drawings.


 * Definitions**
 * __Vanishing Point:__ A vanishing point is the point where parallel lines appear to meet which is often on what is called the horizon.
 * __Theorem- Sets of Parallel Lines:__ In a perspective drawing, all the lines that are parallel to each other, but not parallel to the picture plane, meet at one point that is known as a vanishing point.
 * __Theorem- Lines Parallel to the Ground:__ In any perspective drawing, a line that is in the plane of the ground of the drawing but is not parallel to the picture plane will meet the horizon of the drawing. Any line parallel to that line will meet the horizon of the drawing at the same point.