Unit 1 test: Foundations of Geometry

Two distinct planes intersect. Their intersection is

Seven points lie in a plane, and no three of them are collinear. How many different lines pass through at least two of the points?

Points $A$, $B$ and $C$ lie on a line in that order. Which two rays are opposite rays?

$B$ is between $A$ and $C$, with $AB = 3x + 1$, $BC = 2x + 4$ and $AC = 30$. Find $AB$.

Find the distance between $(-1, 3)$ and $(5, 11)$.

Find the midpoint of the segment joining $(-3, 8)$ and $(7, -2)$.

$M(3, -2)$ is the midpoint of $\overline{AB}$, and $A = (-1, 4)$. Find the coordinates of $B$.

$M$ is the midpoint of $\overline{AB}$, with $AM = 6x - 4$ and $MB = 4x + 6$. Find $AB$.

$\overrightarrow{BD}$ bisects $\angle ABC$, and $m\angle ABD = 48^\circ$. How is $\angle ABC$ classified?

$D$ is in the interior of $\angle ABC$, with $m\angle ABD = (2x + 5)^\circ$, $m\angle DBC = (4x - 11)^\circ$ and $m\angle ABC = 120^\circ$. Find $m\angle DBC$ in degrees.

Find the measure, in degrees, of the supplement of the complement of a $25^\circ$ angle.

Two vertical angles measure $(6x - 15)^\circ$ and $(4x + 25)^\circ$. Find the measure of each angle in degrees.

Two angles form a linear pair, and one is $4$ times the other. Find the measure of the larger angle in degrees.

Which construction locates the midpoint of a segment?

In the perpendicular bisector construction for $\overline{AB}$, $AB = 10$ and the compass is set to $13$. How far apart are the two points where the arcs cross?