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Chapter 10: Problem 71

Describe everyday objects that approximate points, lines, and planes.

Short Answer

Expert verified
Everyday objects that approximate: a point could be the tip of a needle, a line could be the edge of a ruler, and a plane could be the surface of a tabletop.

Step by step solution

01

Identifying Everyday Objects that resemble Points

The most useful approximation of a point in everyday life would be anything that is perceived as having a single position with no dimensions. Examples of this could be the tip of a needle, the dot from a greased paint marker, or even the tiny period at the end of a sentence in a book.
02

Identifying Everyday Objects that resemble Lines

Lines are things that extend indefinitely in two directions and are often understood as linear objects. In daily life, a line can be approximated by objects like uncooked spaghetti or long strings. The edge of a ruler, or the long and straight white or yellow road markers on a highway can also serve as examples for lines.
03

Identifying Everyday Objects that resemble Planes

In geometry, a plane is a flat, two-dimensional surface that extends infinitely far. Close approximations of this in the real world could include objects like a tabletop, the surface of a calm lake, a wall or even a chalkboard.

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In the diagram for Exercises \(17-19\), suppose that you are not told that \(\triangle A B C\) and \(\triangle A D E\) are similar. Instead, you are given that \(\overleftrightarrow{E D}\) and \(\overleftrightarrow{C B}\) are parallel. Under these conditions, explain why the triangles must be similar.

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