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Geometry

Ray C. Jurgensen,Richard G. Brown,John W. Jurgensen

Chapter 1

Points, Lines, Planes, and Angels

Educators


Problem 1

Copy and complete the table. Refer to the diagrams on pages 1 and 2 .
$$\begin{array}{cc} \text { Distance between } & \text { Diagram distance } & \text { Ground distance } \\ {X \text { and } P} & {\underline{5} \text {cm}} & {\underline{10} \text {cm}} \\ {X \text { and } F} & {\underline{7} \text {cm}} & {\underline{?} \text {cm}} \\ {X \text { and } T} & {\underline{?} \text {cm}} & {\underline{?} \text {cm}} \\ {Y \text { and } F} & {\underline{?} \text {cm}} & {\underline{19} \text {cm}} \\ {F \text { and } T} & {\underline{12} \text {cm}} & {\underline{?} \text {cm}}\end{array}$$

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Problem 2

For Exercises 2-4 use a centimeter ruler. If you don't have a centimeter ruler, you may use the centimeter ruler shown below as a guide. Either open your compass to the appropriate.
Copy the points $F . T,$ and $P$ from the diagram on page 2 . If you lay you paper over the page, you can see through the paper well enough to get the points.
a. Draw a line to indicate all points equidistant from $F$ and $T$ .
b. Draw a circle to indicate points 6 $\mathrm{cm}$ from $P$ . If you don't have a compass, draw as well as you can freehand.
c. How many points are equidistant from $F$ and $T$ , and are also 6 $\mathrm{cm}$ from $P ?$

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Problem 3

For Exercises 2-4 use a centimeter ruler. If you don't have a centimeter ruler, you may use the centimeter ruler shown below as a guide. Either open your compass to the appropriate.
Repeat Exercise $2 .$ but use 2 $\mathrm{cm}$ instead of 6 $\mathrm{cm} .$

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Problem 4

For Exercises 2-4 use a centimeter ruler. If you don't have a centimeter ruler, you may use the centimeter ruler shown below as a guide. Either open your compass to the appropriate.
There is a distance you could use in parts (b) and (c) of Exercise 2 that would lead to the answer one point in part (c). Estimate that distance.

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Problem 5

Which is greater, the distance from $R$ to $S$ or the distance from $T$ to $U ?$

Evan S.
Numerade Educator

Problem 6

Which is greater, the distance from $A$ to $B$ or the distance from $A$ to $C ?$

Evan S.
Numerade Educator

Problem 7

How does the area of the outer square compare with the area of the inner square?

Evan S.
Numerade Educator

Problem 8

Compare the areas of the red and blue regions. (Area of circle $=\pi r^{2} . )$

Evan S.
Numerade Educator

Problem 9

In the diagram $a, b, c,$ and $d$ are lengths. Which is greater, the product ab or the product $c d ?$

Evan S.
Numerade Educator

Problem 10

A path between opposite vertices of the square is made up of hundreds of horizontal and vertical segments. (The diagram shows a simplified version.) What is the best approximation to the length of the path—24, 34, 44, or more than 44?

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