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Objectives

6.1 Solid Shapes. Objectives. 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. isometric drawing orthographic projection. 6.1 Solid Shapes.

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Objectives

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  1. 6.1 Solid Shapes Objectives • 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.

  2. isometric drawing orthographic projection 6.1 Solid Shapes Glossary Terms

  3. 6.1 Solid Shapes Key Skills Create isometric drawings of solid figures. Make an isometric drawing of the solid on grid paper.

  4. 6.1 Solid Shapes Key Skills Draw orthographic projections of solid figures. Draw the six orthographic views of the solid shown.

  5. TOC 6.1 Solid Shapes Key Skills Find the volume and surface area of solids that are composed of cubes. Find the volume and surface area of this solid. Volume = 5 cubic units Surface Area = 22 square units

  6. 6.2 Spatial Relationships Objectives • Define polyhedron. • Identify the relationships among points, lines, segments, planes, and angles in three-dimensional space. • Define dihedral angle.

  7. 6.2 Spatial Relationships Theorems, Postulates, & Definitions Polyhedron: A polyhedron is a closed spatial figure composed of polygons, called the faces of the polyhedron. The intersections of the faces are the edges of the polyhedron. The vertices of the faces are the vertices of the polyhedron.

  8. 6.2 Spatial Relationships Theorems, Postulates, & Definitions Dihedral Angle: A dihedral angle is the figure formed by two half-planes with a common edge. Each half-plane is called a face of the angle, and the common edge of the half-planes is called the edge of the angle. Parallel Planes: Two planes are parallel if and only if they do not intersect.

  9. Skew edges: AB and RC RC is perpendicular to ABCDE. TOC 6.2 Spatial Relationships Key Skills Identify relationships among lines and planes in space. Parallel faces: ABCDE and PQRST Perpendicular faces: ABCDE and BCRQ

  10. d =  l2 + w2 + h2 . 6.3 Prisms Theorems, Postulates, & Definitions Diagonal of a Right Rectangular Prism 6.3.1: In a right rectangular prism with dimensions l  w  h,the length of a diagonalis given by:

  11. Lateral edge: BQ 6.3 Prisms Key Skills Identify parts of a prism. Bases: ABCD and PQRS Lateral face: ABQP

  12. d = 102 + 122 + 152 = 469  21.66 feet TOC 6.3 Prisms Key Skills Find the length of a diagonal of a right rectangular prism. Find the length of a diagonal of a right rectangular prism that has length 10 feet, width 12 feet, and height 15 feet.

  13. d = (x2  x1)2 + (y2  y1)2 + (z2  z1)2 . y1 + y2 z1 + z2 x1 + x2 , . , 2 2 2 6.4 Coordinates in Three Dimensions Theorems, Postulates, & Definitions Distance Formula in Three Dimensions 6.4.1: The distance, d, between the points (x1, y1, z1) and (x2, y2, z2) is given by: Midpoint Formula in Three Dimensions 6.4.2: The midpoint of a segment with endpoints at (x1, y1, z1) and (x2, y2, z2) is given by:

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