2memgus

[[image:Isometric_city_picture.jpg]]Shapes that are Solid
There is a certain type of graph paper that will really help people who are just starting to draw isometric drawings. It is called Isometric Dot Paper. The paper has diagonal rows of dots that form a 30° angle with horizontal lines also formed. You can do some fun activites and gain further knowledge by clicking [|Here]
 * Objectives**
 * Using a piece of isometric dot paper, draw three-dimensional shapes made of cubes.
 * Create an understanding of the six orthographic projections.
 * Create a basic understanding of the volume and surface area of isometric cube drawings.
 * Isometric Dot Paper**
 * Definitions**
 * __Isometric Drawing:__ is a type of a three-dimensional drawing.
 * __Orthographic Projection:__ the different views of an object where points of the object are being projected.

The Spatial Relationships[[image:205909352_f5e994369b_m.jpg width="100" height="89"]]

 * Objectives**

[|Here]is a link that will take you to a website with more detailed descriptions of polyhedrons.
 * Define the term: Polyhedron.
 * Identify the relationships with points, segments, lines, angles, and planes in a three-dimensional place.
 * Define the term: dihedral angle.
 * Definitions**
 * A polyhedron is a spatial figure made up of faces, also called polygons.
 * A dihedral angle is the figure made up by two half-planes with a common edge.
 * Two planes can be parallel if and only if they never intersect.
 * A line can be perpendicular to a plane if and only if it is perpendicular to every line in the plane that goes through P
 * A line that is not contained in a given plane can only be parallel to a plane if an only if it is parallel to a line that is in the given plane.
 * The measure of a dihedral angle is the measure of an angle that formed by two rays that are on the two faces of the planes and that are perpendicular to the edge.

Gus's Prisms[[image:486035954_e532747eb5.jpg width="85" height="79"]]
Faces that are formed by a polygonal region and its image are each called a base of a prism. The rest of the faces on the polygon are called Lateral Faces. Diagonal of a Right Rectangular Prism: In the Right rectangular prism that has dimensions L x W x H, the length of the diagonal is diven by: (L^2 x W^2 x H^2)square rooted. There is more detailed information on Prisms, and some more pictures, if you click [|Here]
 * Objectives**
 * Define the terms: Right Prism, Prism, and Oblique Prism.
 * Examine the shapes of prisms and lateral faces.
 * Solve the problems by using the diagonal measure of a right prism.
 * Definitions**
 * A prism is a polyhedron that is made up of a polygonal area and its translated image on a parallel plane.
 * One other type of prism is a "Right Prism" where all of the lateral faces are rectangles.
 * The last type of prism is "Oblique Prism" which has at least one nonrectangular lateral face

Different Coordinates in 3-D[[image:269262129_dd0c74c239.jpg width="76" height="74"]]
A 3-D Coordinate plane has 3 axes vs. 2. A x, y, and z axes'. A way to represent this with your hand, is to let your index finger represent the x axes, let your middle finger represent the y axes, and let your thumb represent the z axes. The positive direction for the X axes, is for it to be pointing down, and to the left. The positive direction for the z axes is for it to be pointing straight up, And the positive direction for the y axes is for it to be point straight to the right. You can get some more information and some examples of a 3-D coordinate plane by clicking [|here]
 * Objectives**
 * Recognize the features of a 3-D coordinate system, including the x,y, and z axes, the four octants, and coordinate planes.
 * Solve some problems by using the distance formula in 3-D.
 * 3-D Coordinate Plane**

theorem: Sets of Parallel Lines, In a perspective drawing, all of the lines that are parallel to each other meet at a single point that is known as a vanishing point. Theorem: Lines Parallel to the ground, In a perspective drawing, a line that is in the plane of the ground that is in the drawing and is not parallel to the picture plane will meet in the horizon of the drawing.
 * Objectives**
 * Define and identify the basic concepts of the perspective drawings.
 * Apply the basic concepts here to create your own drawings.