ACT 1 Geo: Identify similar figures

$Q_{1}:$ A relationship that compares the relative size of two amounts is ?

$Q_{2}:$ The ratio of $x$ to $y$ is $5:2$. If $y = 12$, then $x =$

$Q_{3}:$ If $y=\frac{1}{24}$ and $\frac{x}{ \frac{1}{2} }=\frac{\frac{1}{3}}{y}$, then $x=$

$Q_{4}:$ If a jar contains nickels, dimes, and quarters in the ratio of $2:5:7$, what is the ratio of nickels to the total number of coins?

$Q_{5}:$ If $\frac{x-1}{y-2}=\frac{3}{5}$ and $y=x+3$, what is the value of $x$?

$Q_{6}:$ Triangles $ABC$ and $DEF$ are similar; vertices $D, E,$ and $F$ correspond to vertices $A, B,$ and $C$. The measure of angle $B$ is $90$ degrees, the length of $BC$ is $24\sqrt{3}$, and $sin C = 0.5$. The lengths of the sides of triangle $ABC$ are $1.5$ times those of triangle $DEF$. What is the length of side $DE$?

$Q_{7}:$ The area of the rhombus $TUVW$ in figure below is

$Q_{8}:$ If the ratio of the lengths of segment $\overline{AB}$ to segment $\overline{CD}$ is $3:5$ and $\overline{AB}=15$cm, find the measure of segment $\overline{CD}$.

$Q_{9}:$ The measures of the angles of a triangle are in the ratio of $2:3:4$. Find the measure of the smallest angle.

$Q_{10}:$ The ratio $\frac{2x^{2}-18}{x-3}$ in simplest form is?

$Q_{11}:$ Given $\Delta AMN \sim \DeltaABC$, find $\overline{BC}$.

$Q_{12}:$ The perimeter of a rectangle is $48$ cm. If the ratio of its width to length is $1:3$, then what is its length?

$Q_{13}:$ A rectangular prism has a length of $15$ cm, a width of $9$ cm, and a height of $6$ cm. If each dimension is divided by $3$, what is the ratio of the volume of the original prism to the second prism?

$Q_{14}:$ If two similar octagons have a scale factor of $3:5$, then the ratio of their areas is

$Q_{15}:$ The ratio of the measures of the angles of a quadrilateral is $1:2:4:5$. What is the measure of the largest angle?

$Q_{16}:$ In Figure below, if $AC \parallel GE$ and $GF = x$ and $FE = y$, then the ratio area$\frac{\Delta BCD}{\Delta BCA}=$

$Q_{17}:$ If the ratio of $sec x$ to $csc x$ is $1 : 4$, then the ratio of $tan x$ to $cot x$ is

$Q_{18}:$ A right triangle has sides in the ratio of $5 : 12 : 13$. What is the measure of the smallest angle in the triangle, in degrees?

$Q_{19}:$ : If $2 ^{a}= 3^{ b}$ , what is the ratio of $a$ to $b$?

$Q_{20}:$ The base of pyramid $1$ is a $3:4:5$ triangle, and the base of pyramid $2$ is a square whose sides are $3$. If the volumes of the pyramid are equal, what is the ratio of the height of pyramid $1$ to the height of pyramid $2$?

$Q_{21}:$ If in the figure below, the ratio of $a$ to $b$ is $3$ to $2$, then what is the value of $a + b $?

$Q_{22}:$ The ratio of $x$ to $y$ is $5$ to $12$. If $x$ is $45$, what is the value of $y$?

$Q_{23}:$ Each side of square $A$ has a length of $3$ meters, while each side of square $B$ has a length of $9$ meters. What is the ratio of the area of square $A$ to the area of square $B$?

$Q_{24}:$ The ratio of the lengths of each of the sides of a triangle is $4:12:14$. If the shortest side has a length of $2$ feet, what is the perimeter of the triangle in feet?

$Q_{25}:$ In figure below, the ratio of the lengths of $AB$ to $BC$ of rectangle $ABCF$ is $2:3$, and $C$ is the midpoint of $DF$. If $AF = FE$, what is the area of triangle $DEF $?

$Q_{26}:$ If the ratio of $A$ to $B$ is $3:8$ and the ratio of $B$ to $C$ is $1:6$, what is the ratio of $A$ to $C $?

$Q_{27}:$ If the ratio of $x$ to $y$ is $1:6$, what is the difference between $y$ and $x$ when $x = 12$?