2marmat

=3-Dimentional shapes=


 * Objectives:**
 * Use dot paper to draw 3-D shapes.
 * Develop an understanding of orthographic projections.
 * Develop an understanding of surface area and volume.

http://illuminations.nctm.org/ActivityDetail.aspx?ID=125
 * Isometric Drawing** - Horizontal lines represented by lines that form 30°angles in the picture
 * Orhtographic Projection -** is a view of an object where the object becomes "projected" onto the picture plane along perpendicular lines to the picture plane.

=Spatial Relationships=


 * Objectives:**
 * Define polyhedron
 * Identify the relationships amoung lines, points, planes, segments, and angles
 * Define dihedral angle

A //polyhedron// is a closed spatial object made of polygons, called the //faces// of the polyhedron. The intersections of the faces are known as the //edges// of the polyhedron. The verticies of the faces are the //verticies// of the polyhedron.
 * Polyhedron:[[image:205909352_f5e994369b_m.jpg width="233" height="166" align="right" link="http://www.flickr.com/photos/iangallagher/205909352/"]]**

http://mathworld.wolfram.com/Polyhedron.html


 * Parallel Planes:** Two planes are parallel if and olnly if they do not intersect.


 * A line perpendicular to a plane:** A line is perpendicular to a plane at point R if and only if it is perpendicular to every line in the plane that intersects point R.


 * 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 any line that is in the plane.


 * Dihedral Angle:** A dihedral angle is a figure formed by two half-planes with the same edge. Each half-plane is called a face of the angle, and the common edge of the half-plane is called an edge of an angle.


 * Measure of a dihedral angle:** The measure of a dihedral angle is the measure of an angle that are on the faces and that are perpendicular to the edge.

=Prisms=

.
 * Objectives:**
 * Define prism, right prisms, and oblique prisms
 * Look at the shapes of lateral faces of prisms
 * Solve problems by using diagonal measurement of a right prism
 * Prism-** is a polyhedron that consists of a polygonal regionand its translated image on a plane, wih quadrilateral faces connecting the corresponding edges.
 * Base-** The faces formed by the polygonal region and its image.


 * Lateral faces-** The remaining faces, that are quadrilaterals.


 * Lateral edges-** The edges of the lateral faces that arn't edges of either base.


 * Right Prism-** is a prism where all lateral faces are rectangles.


 * Oblique Prism-** has at least one lateral face that is not a rectangle.

http://www.literka.addr.com/list.htm
 * Diagonal of a polyhedron**- a segment were the endpoints are vertices of two different faces on the polyhedron.

In A right rectangular prism with the dimensions lenght x width x height, the length of a diagonal is d= the square root of length² × width² × height².
 * Diagonal of a right rectangular prism**

=Coordinates in Three Dimensions=


 * Objectives:**
 * Identify the features of a three-dimensional coordinate system, the axes, octants, and coordinate planes.
 * Solve problems by using the distance formula in three dimensions.


 * Right-handed system-** The arrangement of the axes.

http://www.mathwords.com/o/octants.htm
 * Octant-** One of the eight spaces into a three-dimensional coordinate system is divided by xy-yz-xz-planes.


 * Coordinate plane-** A grid formed by two or more coordinatized lines that are known as axes, that intersect at right angles at a point that is called the origin.

=Perspective Drawing=


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


 * Vanishing point-** The point at which parallel segments of a depicted object will meet if they are extended.

In a persective drawing, all lines that are parallel to one another, but not to the picture plane, meet at a single point known as a vanishing point.
 * Theorem: Sets Of Parallel Lines:**

In a perspective drawing, a line that is in the plane of the ground in the drawing and is not parallel to the picture plane will meet at the horizon of the drawing. Any line parallel to this line will meet the horizon of the drawing at the same point.
 * Theorem: Lines Parallel To The Ground:**