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Chapter 13

Geometry

Educators


Problem 1

Which of the following could be the degree measures of two angles in a right triangle? Indicate all such angles.
a. $20^{\circ}$ and $70^{\circ}$
b. $30^{\circ}$ and $60^{\circ}$
c. $45^{\circ}$ and $45^{\circ}$
d. $55^{\circ}$ and $55^{\circ}$
e. $75^{\circ}$ and $75^{\circ}$

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Problem 2

What is the perimeter of the figure above?
a. 51
b. 64
c. 68
d. 77
e. 91

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Problem 3

$$\begin{array}{c}A B=B C=E G \\F G=8\end{array}$$
$$\begin{array}{cc} \text{Quantity A} && \text{Quantity B} \\ \text{The area of square A B C D} && 32 \end{array}$$
a. Quantity $\mathrm{A}$ is greater.
b. Quantity $\mathrm{B}$ is greater.
c. The two quantities are equal.
d. The relationship cannot be determined from the information given.

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Problem 4

$(a, 6)$ is a point (not shown) in Quadrant I
$(-6, b)$ is a point (not shown) in Quadrant II.
$$\begin{array}{cc}\text { Quantity } \mathbf{A} & \text { Quantity } \mathbf{B} \\ a & b\end{array}$$
a. Quantity $\mathrm{A}$ is greater.
b. Quantity $\mathrm{B}$ is greater.
c. The two quantities are equal.
d. The relationship cannot be determined from the information given.

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Problem 5

A piece of twine with length of $t$ is cut into two pieces. The length of the longer piece is 2 yards greater than 3 times the length of the shorter piece. Which of the following is the length, in yards, of the longer piece?
a. $\frac{t+3}{3}$
b. $\frac{3 t+2}{3}$
c. $\frac{t-2}{4}$
d. $\frac{3 t+4}{4}$
e. $\frac{3 t+2}{4}$

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Problem 6

The circle with center $D$ is drawn inside the circle with center $C,$ as shown in the figure above. If $C D=3,$ what is the area of semicircle $E A B ?$
a. $\frac{9}{2} \pi$
b. $9 \pi$
c. $12 \pi$
d. $18 \pi$
e. $36 \pi$

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Problem 7

For the final exam in a scuba diving certification course, Karl navigates from one point in a lake to another. Karl begins the test $x$ meters directly beneath the boat and swims straight down toward the bottom of the lake for 8 meters. He then turns to his right and swims in a straight line parallel to the surface of the lake and swims 24 meters, at which point he swims directly from his location, in a straight line, back to the boat. If the distance that Karl swims back to the boat is 26 meters, what is the value of $x ?$

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Problem 8

$$\begin{array}{cc}\text { Quantity } \mathbf{A} & \text { Quantity } \mathbf{B} \\ \text{The circumference of a circular region with radius r} & \text{The perimeter of a square with side r}\end{array}$$
a. Quantity A is greater.
b. Quantity B is greater.
c. The two quantities are equal.
d. The relationship cannot be determined from the information given.

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Problem 9

Triangle $A B C$ is contained within a circle with center $C .$ Points $A$ and $B$ lie on the circle. If the area of circle $C$ is $25 \pi,$ and the measure of angle $A C B$ is $60^{\circ},$ which of the following are possible lengths for side $A B$ of triangle $A B C ?$ Indicate all such lengths.
a. 3
b. 4
c. 5
d. 6
e. 7

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Problem 10

$$\begin{array}{cc}\text { Quantity } \mathbf{A} & \text { Quantity } \mathbf{B} \\ x & 5.9 \end{array}$$
a. Quantity A is greater.
b. Quantity B is greater.
c. The two quantities are equal.
d. The relationship cannot be determined from the information given.

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Problem 11

$$\begin{array}{cc}\text { Quantity } \mathbf{A} & \text { Quantity } \mathbf{B} \\ f & g \end{array}$$
a. Quantity A is greater.
b. Quantity B is greater.
c. The two quantities are equal.
d. The relationship cannot be determined from the information given.

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Problem 12

Given points $A(2,3)$ and $B(x, y)$ in the rectangular coordinate system above, if $y=4.2,$ then $x=$
a. 2.6
b. 2.8
c. 2.9
d. 3.0
e. 3.2

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Problem 13

In rectangle $A B C D$ above, which of the following is the area of the triangle $A B D ?$
a. 6
b. 7.5
c. 10
d. 12
e. 15

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Problem 14

$$\begin{array}{cc}\text { Quantity } \mathbf{A} & \text { Quantity } \mathbf{B} \\ \text { The area of triangle } AOB & \text{The area of the shaded region} \end{array}$$
a. Quantity A is greater.
b. Quantity B is greater
c. The two quantities are equal.
d. The relationship cannot be determined from the information given.

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Problem 15

The circumference of the circle with center $O$ shown above is $15 \pi$ LMNO is a parallelogram and $\angle O L M=108^{\circ} .$ What is the length of minor arc $A B$?
a. $15 \pi$
b. $9 \pi$
c. $3 \pi$
d. $2 \pi$
e. $\pi$

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