Unit 2 test: Reasoning and Proof

Find the next number in the pattern: $29, 21, 13, 5, \dots$

Which is a counterexample to the conjecture "The product of two numbers is always greater than either number"?

Given: "If two angles are vertical angles, then they are congruent" and "$\angle 5$ and $\angle 6$ are vertical angles." What can you conclude, and by which law?

What is the inverse of "If a figure is a triangle, then it has three sides"?

The conditional "If $x = -4$, then $x^2 = 16$" is true. Which related statement is false?

Which statement can be written as a true biconditional?

Which property justifies: If $m\angle A = m\angle B$, then $m\angle B = m\angle A$?

In this algebraic proof, which reason justifies step 2?

Point $B$ is between $A$ and $C$. If $AB = 3x - 2$, $BC = 2x + 7$ and $AC = 30$, find $BC$.

$\overrightarrow{BD}$ bisects $\angle ABC$. If $m\angle ABD = 5x - 4$ and $m\angle DBC = 3x + 8$, find $m\angle ABD$ in degrees.

Given: $M$ is the midpoint of $\overline{AB}$. Prove: $AM = MB$. Which reason belongs in step 3?

Two lines intersect. One angle measures $133^\circ$. What is the measure, in degrees, of each angle that forms a linear pair with it?

Vertical angles measure $(7x - 20)^\circ$ and $(4x + 25)^\circ$. Find the measure of each angle, in degrees.

Given: $\angle 1$ and $\angle 2$ are complementary; $\angle 3$ and $\angle 2$ are complementary. Which theorem proves $\angle 1 \cong \angle 3$?

$\angle 1$ and $\angle 2$ form a linear pair, and $m\angle 1$ is $4$ times $m\angle 2$. $\angle 3$ is vertical to $\angle 1$. Find $m\angle 3$ in degrees.