Instructions: Choose the best answer for each question. Show your work where appropriate.

Which of the following best describes a trapezoid?

If two parallel lines are intersected by a transversal, and one of the consecutive interior angles measures $70^{\circ}$, what is the measure of the other consecutive interior angle?

Which postulate or theorem can be used to prove that two right triangles are congruent if their hypotenuses and a pair of corresponding legs are congruent?

Which of the following is always true for a parallelogram?

A triangle has a base of $15\text{ cm}$ and a height of $8\text{ cm}$. What is its area?

What is the volume of a cylinder with a radius of $5\text{ cm}$ and a height of $4\text{ cm}$? Use $\pi$.

What is a chord of a circle?

An inscribed angle in a circle intercepts an arc that measures $50^{\circ}$. What is the measure of the inscribed angle?

In a right triangle, the side opposite angle $A$ is $6\text{ m}$ and the hypotenuse is $8\text{ m}$. What is the approximate length of the side adjacent to angle $A$?

Which of the following is a unique property of a rhombus that is not necessarily true for all parallelograms?

Two triangles have corresponding angles that are congruent. These triangles must be:

A right triangle has legs of length $5$ and $12$. What is the length of the hypotenuse?

Instructions: Provide detailed solutions or explanations for each question. Show all necessary calculations.

Calculate the area of the shaded region, which is a semicircle. Round your answer to two decimal places. Use $\pi \approx 3.14159$.

A spherical ball has a radius of $6\text{ cm}$. Calculate its volume. Express your answer in terms of $\pi$.

A trapezoid has parallel bases measuring $15\text{ cm}$ and $21\text{ cm}$. What is the length of its median?

In parallelogram $ABCD$, $AB = 2x+5$ and $CD = 3x-5$. Also, $m\angle A = (4y)^{\circ}$ and $m\angle C = (y+105)^{\circ}$. Find the values of $x$ and $y$.

A circle has a radius of $10\text{ cm}$. Find the length of an arc intercepted by a central angle of $90^{\circ}$. Round your answer to two decimal places. Use $\pi \approx 3.14159$.

From a point on the ground $10\text{ m}$ away from the base of a flagpole, the angle of elevation to the top of the flagpole is $60^{\circ}$. Calculate the height of the flagpole to two decimal places.

Point $P$ is outside a circle. A tangent segment $PQ$ is drawn from $P$ to the circle, and the radius at $Q$ is $5\text{ cm}$. If the distance from $P$ to the center of the circle is $13\text{ cm}$, find the length of $PQ$.

A triangle has vertices at $A(1,1)$, $B(11,1)$, and $C(6,7)$. Calculate the area of the triangle.

Given points $A(1,2)$ and $B(7,10)$, find the coordinates of the midpoint of segment $AB$ and the distance between $A$ and $B$.

Instructions: For each problem, write a complete two-column proof. Clearly state your Given, Prove, and provide logical Statements and Reasons.

Given: $\overline{AB} \cong \overline{DE}$, $\angle A \cong \angle D$, $\angle B \cong \angle E$. Prove: $\triangle ABC \cong \triangle DEF$.

Given: Line $l$ is parallel to line $m$. Line $t$ is a transversal. Prove: $\angle 1 \cong \angle 3$ (Alternate Interior Angles are congruent).

Given: $ABCD$ is a parallelogram. Prove: Opposite sides of a parallelogram are congruent ($\overline{AB} \cong \overline{CD}$ and $\overline{BC} \cong \overline{DA}$).

Given: $\overline{PQ}$ and $\overline{PR}$ are tangent segments to circle $O$ from external point $P$. Prove: $\overline{PQ} \cong \overline{PR}$.

Given: $\triangle ABC$ is isosceles with $\overline{AB} \cong \overline{AC}$. $\overline{AD}$ is the angle bisector of $\angle BAC$. Prove: $\overline{BD} \cong \overline{CD}$.