Algebra In $\triangle P Q R, \angle S Q R \cong \angle S R Q, P Q>P R, \mathrm{~m} \angle P S R=(4 y+9)^{\circ}$ and $\mathrm{m} \angle Q S P=(6 y-24)^{\circ}$. Find the range of values for $y$.

In $\triangle D E F, F$ is a right angle, $\mathrm{m} \angle D=45^{\circ}$, and $D E=3$ centimeters.
Draw a diagram of $\triangle D E F$.

Analyze Write a paragraph proof of the following:
Given: Ray $F D$ bisects $\angle E F C$, ray $F C$ bisects $\angle D F B$ Prove: $\angle E F D \cong \angle C F B$

Analyze For what natural-number values of n does the equation $y=x^n$ have a line of symmetry?

Error Analysis Giselle states that since the tile on the right is divided into three sections, there is a one-in-three chance of a fly randomly landing on any section. Is she correct? Explain.

If quadrilateral M N P R has three sides of equal length- M N, N P, and P R-must the quadrilateral be a parallelogram?

Write Explain why the AA Postulate could also be called the AAA Postulate.

In the proportion $\dfrac{15}{6}=\dfrac{8}{y}$, what is the value of $y$ ?

Quadrilateral L M N O is similar to quadrilateral $B C D E$. If $\mathrm{m} \angle B=65^{\circ}$, $\mathrm{m} \angle C=125^{\circ}, \mathrm{m} \angle D=50^{\circ}$, and $\mathrm{m} \angle E=120^{\circ}$, what is the measure of each angle in quadrilateral $L M N O$ ?

The ratio of the length of a rectangle to its width is $7: 3$. If the width of the rectangle is 42 centimeters, what is the length?

Write Explain how to find the other two side lengths of a $30^{\circ}-60^{\circ}-90^{\circ}$ right triangle if you only know the length of the shorter leg.

What is the resultant vector of $c$ and $d$, in component form?

Name a type of triangle that has exactly one line of symmetry.

The unit circle and $\odot C$ with a radius of $r$ are concentric. Circle $D$ with a radius of $s$ is centered at $(8,0)$. If circles $C$ and $D$ touch at one point, write all possible relations between $r$ and $s$.