Nets & Drawings for Visualizing Geometry

Section 1-1

Vocab

• Polyhedron - 3-dimensional figure whose surfaces are polygons

• Face of polyhedron - each polygon that forms the polyhedron

• Edge - segment formed by the intersection of two faces

• Vertex - point where 3 or more edges intersect

Vocab Ctd.

Vocab Ctd.

• Net - 2-dimensional pattern that you can fold to form a 3-dimensional figure

Identifying a NetIs the pattern a net for a cube? If so, name two letters that will

be on opposite faces.

The pattern is a net because you can fold it to form a cube. Fold squares A and C up to form the back and front of the cube. Fold D up to form a side. Fold E over to form the top. Fold F down to form another side.

A and C are the back and front faces.

After the net is folded to form a cube, the following pairs of letters are on opposite faces:

B and E are the bottom and top faces.

D and F are the right and left side faces.

You try

Drawing a NetDraw a net for the figure with a square base and four

isosceles triangle faces. Label the net with its dimensions.

Think of the sides of the square base as hinges, and “unfold” the figure at these edges to form a net.The base of each of the four isosceles triangle faces is a side of the square.

New Vocab

• Isometric drawing - shows 3 sides of a 3-dimensional object from a corner view

• Orthographic - presents a 3-dimensional figure as a top view, front view, and right side view

Isometric DrawingMake an isometric drawing of the cube structure below.

You will draw all the edges of the figure that you can see.

Start by drawing the front face of the figure.

Next, draw the back edges of the figure.

Finally, fill in the right face, top faces, and left edges.

(continued)

You try

• Create an isometric drawing of the figure

Orthographic Drawing

Make an orthographic drawing of the isometric drawing below.

Orthographic drawings flatten the depth of a figure.

An orthographic drawing shows three views.

Because no edge of the isometric drawing is hidden in the top, front, and right views, all lines are solid.

You try

• Make an orthographic drawing from the isometric drawing.

Closure

• Explain how isometric & orthographic drawings are alike and how they are different.

• All show 3-d figures on a 2-d surface; isometric drawings show 3 faces, while orthographic drawing show the outlines of 3 views.