1-1 Nets and Drawings for Visualizing Geometry

Quick Review

A net is a two-dimensional pattern that you can fold to form a three-dimensional figure. A net shows all surfaces of a figure in one view.

An isometric drawing shows a corner view of a three-dimensional object. It allows you to see the top, front, and side of the object in one view.

An orthographic drawing shows three separate views of a three-dimensional object: a top view, a front view, and a right-side view.

Example

Draw a net for the solid below.

Exercises

5. The net below is for a number cube. What are the three sums of the numbers on opposite surfaces of the cube?

   

6. Make an orthographic drawing for the isometric drawing below. Assume there are no hidden cubes.

   
   Image Long Description

1-2 Points, Lines, and Planes

Quick Review

A point indicates a location and has no size.

A line is represented by a straight path that extends in two opposite directions without end and has no thickness.

A plane is represented by a flat surface that extends without end and has no thickness.

Points that lie on the same line are collinear points.

Points and lines in the same plane are coplanar.

Segments and rays are parts of lines.

Example

Name all the segments and rays in the figure.

Segments: A B ¯ , A C ¯ , B C ¯ , eh b bar , comma , eh c bar , comma , b c bar , comma  and B D ¯ b d bar

Rays: B A → , C A → b eh vector , comma , c eh vector  or C B → , A C → c b vector , comma , eh c vector  or A B → , B C → , eh b vector , comma , b c vector , comma  and B D → b d vector

Exercises

Use the figure below for Exercises 7–9.

Image Long Description

7. Name two intersecting lines.
8. Name the intersection of planes QRBA and TSRQ.
9. Name three noncollinear points.

Determine whether the statement is true or false. Explain your reasoning.

10. Two points are always collinear.
11. L M → l m vector  and M L → m l vector  are the same ray.

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