Lesson 1.8 – Space Geometry Homework: Lesson 1.8/1-27 Chapter 1 Test Friday 10/18

Learn to draw three-dimensional figures. Identify the parts of three-dimensional figures. Visualize and identify nets of three- dimensional figures. Space Geometry

Edge Face Vertex Three-dimensional figures have faces, edges, and vertices. A face is a polygon or circle an edge is a segment, where two faces meet a vertex is a point, where three or more edges meet

Prisms A prism is –a 3D solid –with two congruent polygon bases that lie in parallel planes –Lateral faces are rectangles (faces connecting the bases) The bases can be any polygon shape The name of the prism is based on the name of the bases. –the prism shown is a triangular prism The bases are triangles and the lateral faces are rectangles

Vertices (points) Edges (lines) Faces (planes) The base has 3 sides.

Vertices (points) Edges (lines) Faces (planes) The base has sides.5

By D. Fisher

Pyramid A pyramid is –a three-dimensional solid – with one polygonal base –lateral sides are triangles –the main vertex is where the lateral sides meet Names of pyramids depending on the shape off the base This is a rectangular pyramid.

Vertices (points) Edges (lines) Faces (planes) The base has sides.4

Vertices (points) Edges (lines) Faces (planes) The base has sides.6

Cylinder A cylinder is a 3D solid 2 bases are congruent circles. –The bases are congruent, parallel circles The smooth lateral face is a rectangle H r

Cone A cone has one circular base The smooth lateral face is part of a circle, less than a semicircle, called a sector The cone has one vertex, at the top H r

Sphere Sphere is the set of all points in space a radius distance from the center of the sphere. A mathematical word for “ball.” A sphere has a radius and diameter, just like a circle does. The size of the sphere is measured by its radius r

Sketching 3D Objects

With your isometric dot paper, sketch the drawing below. Make your box 3 units wide, 2 units high, and 5 units long. After you have sketched the box, try other figures like a cube or pyramid.

Example 1 Try This: Use isometric dot paper to sketch a rectangular box that is 4 units long, 2 units deep, and 3 units tall.

Example 1 Step 1: Lightly draw the edges of the bottom face. It will look like a parallelogram. 2 units by 4 units

Step 2: Lightly draw the vertical line segments from the vertices of the base. 3 units high Example 1 Continued

Step 3: Lightly draw the top face by connecting the vertical lines to form a parallelogram. 2 units by 4 units Example 1 Continued

Step 4: Darken the lines. Use solid lines for the edges that are visible and dashed lines for the edges that are hidden. Example 1 Continued

Drawing a Rectangular Box Use isometric dot paper to sketch a rectangular box that is 5 units long, 3 units deep, and 2 units tall.

Nets A net of a geometric solid is a two-dimensional (planar) figure that can be folded into a geometric solid. Here are a few examples of nets of cubes: However, not every figure of six squares can be folded into a cube. Here are some figures that are not nets of cubes: