# Geometry

## Educators

Problem 1

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

Amrita B.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.
\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}