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[[image:golfer.gif width="36" height="77"]]Solid 3-D Shapes and Orthographic Projections
• Use isometric dot paper to draw three-dimensional shapes composed of cubes. • Develop an understanding of orthographic projection. • Develop a basic understanding of volume and surface area.
 * Objectives:**


 * Isometric Drawing-** is one where the horizontal lines of a shape are represented by lines that form 30 degree angles with a horizontal line somewhere in the picture.


 * Orthographic Projections-** are views of an object in which the 6 sides and bases are "projected" onto a pictue plane along lines perpendiculr to the picture plane.

**[[image:golfer.gif width="38" height="71"]]The Relationships Between Figures In Space.**
•** Define //polyhedron. •// Identify the relationships among points, lines, segments, planes, and angles in three-dimensional space. • Define //dihedral angle.//
 * Objectives:


 * Definition Of Polyhedron:** A closed figure made up of polygons, called the **faces** of the polyhedron. The intersections of the faces of the polygon are called the **edges**. The vertices of the faces are known as the **vertices** of the polyhedron.

•The most used example of a polyhedron is a cube•


 * Definition Of Parallel Planes:** If two lines never intersect, then the lines are parallel.


 * Definition Of A Line Perpendicular to a Plane:** A line is perpendicular to a plane at point //S// if and only if it is perpendicular to every line in the plane that intersects point //S.//


 * Definition Of 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.


 * Half-Plane-** The portion of a plane that sits on one side of a line in the plane anr includes the line.


 * Definition Of Dihedral Angle:** A **Dihedral Angle** is the angle formed by two half-planes with a common edge. Each half-plane is called the **face** of the angle, and the edge that is shared between the half-planes is called the **edge** of the angle.

[|EXPLANATIONS OF DIFFERENT KINDS OF POLYHEDRONS]
 * Definition Of The Measure of a Dihedral Angle:** The measure of an angle formed by two rays that are on the faces that are perpendicular to the edge.

Hudson's Prisims
• Define prism, right prism, and oblique prism. • Examine the shapes of lateral faces of prisms. • Solve problems by using the diagonal measure of a right prism.
 * Objectives:**

A **prism** is a polyhedron made up of a polygonal region and its translated image on a parallel plane. The quadrilateral faces connect to the corresponding edges.

The faces formed by the polygonal region and its image are each called the **bases**. The other quadrilateral faces are called the **lateral faces** of the prism. The edges of the lateral faces that do not touch either base are called the **lateral edges** of the prism.

A **right prism** is where all of the lateral faces are rectangles. An **oblique prism** is where at least one lateral face is nonrectangular. The **Diagonal** of a polyhedronis a segment whose endpoints are vertices of two different faces of the polyhedron.

In a right rectangular prism with the dimensions //l×w×h,// the formula is... d=**//√ l²+w²+l²//
 * Diagonal Of a Right Rectangular Prism Formula:

[|PRISMS WEBSITE]

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

There are 8 octants on a three-dimensional graph. There is a y axes, an x axes, and a z axes. The x and y axes are perpendicular rays that cut each other in half, and the z axis splits the x and y axes in the middle, as shown below... Each pair of axes determines the **Coordinate Plane.

Distance Formula for Three- Dimensions:**
 * d=** √( X2-X1)² + ( Y2-Y1)² + ( Z2-Z1)²

(__X1+X2 ÷ 2__, __Y1+Y2÷2__, __Z1+Z2÷2__)
 * Midpoint Formula for Three- Dimensions:**

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[|THREE-DIMENSIONAL COORDINATES] =Perspective Drawings= • Identify and define the basic concepts of perspective drawing. • Apply these basic caoncepts to create youte own perspective drawing.
 * Objectives**:


 * Vanishing Points** are the places in the horizon where the two parallel lines seem to meet.

In perspective drawings, all the lines that are parallel to each other, but not parallel to the picture plane, meet at a single point known as the vanishing point. In perspective drawings, a line in the plane of the ground in the drawing (not parallel to the picture plane) will always meet at the horizon of the drawing.
 * Sets Of Parallel Lines Theorem.**
 * Lines Parallel to the Ground Theorum:**

•Drawings with only one vanishing point are called **one-point perspective** drawings. •Drawings with two vanishing points are known as **two-point perspective** drawings.

[|THIS WEBSITE WILL HELP YOU BETTER UNDERSTAND HOW TO DRAW PERSPECTIVES.]