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Geometry

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

Chapter 7

Similar Polygons

Educators


Problem 1

$A B C D$ is a parallelogram. Find the value of each ratio.
$A B : B C$

Amrita B.
Numerade Educator

Problem 2

$A B C D$ is a parallelogram. Find the value of each ratio.
$A B : C D$

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Problem 3

$A B C D$ is a parallelogram. Find the value of each ratio.
$m \angle C : m \angle D$

Amrita B.
Numerade Educator

Problem 4

$A B C D$ is a parallelogram. Find the value of each ratio.
$m \angle B : m \angle C$

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Problem 5

$A B C D$ is a parallelogram. Find the value of each ratio.
$A D :$ perimeter of $A B C D$

Amrita B.
Numerade Educator

Problem 6

In Exercises $6-14, x=12, y=10,$ and $z=24 .$ Write each ratio in simplest form.
$x$ to $y$

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Problem 7

In Exercises $6-14, x=12, y=10,$ and $z=24 .$ Write each ratio in simplest form.
$=$ to $x$

Amrita B.
Numerade Educator

Problem 8

In Exercises $6-14, x=12, y=10,$ and $z=24 .$ Write each ratio in simplest form.
$x+y$ to $z$

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Problem 9

In Exercises $6-14, x=12, y=10,$ and $z=24 .$ Write each ratio in simplest form.
$\frac{x}{x+z}$

Amrita B.
Numerade Educator

Problem 10

In Exercises $6-14, x=12, y=10,$ and $z=24 .$ Write each ratio in simplest form.
$\frac{x+y}{z+y}$

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Problem 11

In Exercises $6-14, x=12, y=10,$ and $z=24 .$ Write each ratio in simplest form.
$\frac{y+z}{x-y}$

Amrita B.
Numerade Educator

Problem 12

In Exercises $6-14, x=12, y=10,$ and $z=24 .$ Write each ratio in simplest form.
$x : y : z$

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Problem 13

In Exercises $6-14, x=12, y=10,$ and $z=24 .$ Write each ratio in simplest form.
$z : x : y$

Amrita B.
Numerade Educator

Problem 14

In Exercises $6-14, x=12, y=10,$ and $z=24 .$ Write each ratio in simplest form.
$x :(x+y) :(y+z)$

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Problem 15

Exercises $15-20$ refer to a triangle. Express the ratio of the height to the base in simplest form.
$$
\begin{array}{|c|c|}\hline \text { height } & {5 \mathrm{km}} \\ \hline \text { base } & {45 \mathrm{km}} \\ \hline\end{array}
$$

Amrita B.
Numerade Educator

Problem 16

Exercises $15-20$ refer to a triangle. Express the ratio of the height to the base in simplest form.
$$
\begin{array}{|c|c|}\hline \text { height } & {1 \mathrm{m}} \\ \hline \text { base } & {0.6\mathrm{m}} \\ \hline\end{array}
$$

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Problem 17

Exercises $15-20$ refer to a triangle. Express the ratio of the height to the base in simplest form.
$$
\begin{array}{|c|c|}\hline \text { height } & {0.6 \mathrm{km}} \\ \hline \text { base } & {0.8\mathrm{km}} \\ \hline\end{array}
$$

Amrita B.
Numerade Educator

Problem 18

Exercises $15-20$ refer to a triangle. Express the ratio of the height to the base in simplest form.
$$
\begin{array}{|c|c|}\hline \text { height } & {1 \mathrm{m}} \\ \hline \text { base } & {85\mathrm{cm}} \\ \hline\end{array}
$$

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Problem 19

Exercises $15-20$ refer to a triangle. Express the ratio of the height to the base in simplest form.
$$
\begin{array}{|c|c|}\hline \text { height } & {8 \mathrm{cm}} \\ \hline \text { base } & {50\mathrm{mm}} \\ \hline\end{array}
$$

Amrita B.
Numerade Educator

Problem 20

Exercises $15-20$ refer to a triangle. Express the ratio of the height to the base in simplest form.
$$
\begin{array}{|c|c|}\hline \text { height } & {40 \mathrm{mm}} \\ \hline \text { base } & {0.2\mathrm{m}} \\ \hline\end{array}
$$

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Problem 21

Write the algebraic ratio in simplest form.
$$
\frac{3 a}{4 a b}
$$

Amrita B.
Numerade Educator

Problem 22

Write the algebraic ratio in simplest form.
$$
\frac{2 c d}{5 c^{2}}
$$

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Problem 23

Write the algebraic ratio in simplest form.
$$
\frac{3(x+4)}{a(x+4)}
$$

Amrita B.
Numerade Educator

Problem 24

In Exercises $24-29$ find the measure of each angle.
The ratio of the measures of two complementary angles is $4 : 5 .$

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Problem 25

In Exercises $24-29$ find the measure of each angle.
The ratio of the measures of two supplementary angles is $11 : 4$

Amrita B.
Numerade Educator

Problem 26

In Exercises $24-29$ find the measure of each angle.
The measures of the angles of a triangle are in the ratio $3 : 4 : 5$

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Problem 27

In Exercises $24-29$ find the measure of each angle.
The measures of the acute angles of a right triangle are in the ratio $5 : 7$ .

Amrita B.
Numerade Educator

Problem 28

In Exercises $24-29$ find the measure of each angle.
The measures of the angles of an isosceles triangle are in the ratio $3 : 3 : 2$

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Problem 29

In Exercises $24-29$ find the measure of each angle.
The measures of the angles of a hexagon are in the ratio $4 : 5 : 5 : 8 : 9 : 9 .$

Amrita B.
Numerade Educator

Problem 30

The perimeter of a triangle is 132 $\mathrm{cm}$ and the lengths of its sides are in the ratio $8 : 11 : 14 .$ Find the length of each side.

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Problem 31

The measures of the consecutive angles of a quadrilateral are in the ratio $5 : 7 : 11 : 13 .$ Find the measure of each angle. draw a quadrilateral that satisfies the requirements, and explain why two sides must be parallel.

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Problem 32

What is the ratio of the measure of an interior angle to the measure of an exterior angle in a regular hexagon? A regular decagon? A regular $n$ -gon?

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Problem 33

A team's best hitter has a lifetime batting average of $.320 .$ He has been at bat 325 times.
a. How many hits has he made?
b. The same player goes into a slump and doesn't get any hits at all in his next ten times at bat. What is his current batting average to the nearest thousandth?

Amrita B.
Numerade Educator

Problem 34

A basketball player has made 24 points out of 30 free throws. She hopes to make all her next free throws until her free-throw percentage is 85 or better. How many consecutive free throws will she have to make?

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Problem 35

Points $B$ and $C$ lie on $\overline{A D}$ . Find $A C$ if $\frac{A B}{B D}=\frac{3}{4}, \frac{A C}{C D}=\frac{5}{6},$ and $B D=66$

Amrita B.
Numerade Educator

Problem 36

$$
\begin{aligned} \text { Find the ratio of } x \text { to } y : \frac{4}{y}+\frac{3}{x} &=44 \\ & \frac{12}{y}-\frac{2}{x}=44 \end{aligned}
$$

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