Unit 6 test: Relationships in Triangles

In $\triangle ABC$, $D$ is the midpoint of $\overline{AC}$ and $E$ is the midpoint of $\overline{BC}$. If $DE = 11$, what is $AB$?

In $\triangle ABC$, $\overline{DE}$ is the midsegment parallel to $\overline{AB}$. If $DE = 3x - 2$ and $AB = 4x + 6$, what is $DE$?

Triangle $ABC$ has vertices $A(2, 8)$, $B(-2, 0)$ and $C(4, 6)$. $M$ is the midpoint of $\overline{AB}$ and $N$ is the midpoint of $\overline{AC}$. What is the length of $\overline{MN}$? Give an exact answer.

The midsegment triangle of $\triangle PQR$ has a perimeter of $19$ inches. What is the perimeter of $\triangle PQR$, in inches?

Point $P$ lies on the perpendicular bisector of $\overline{AB}$. If $PA = 6x - 5$ and $PB = 3x + 10$, what is $PA$?

Which point of a triangle is always equidistant from the three sides?

Find the circumcenter of the triangle with vertices $A(0, 0)$, $B(10, 0)$ and $C(4, 6)$.

$I$ is the incenter of $\triangle ABC$. The perpendicular from $I$ to $\overline{AB}$ meets $\overline{AB}$ at $D$. If $ID = 8$ and $IA = 17$, what is $AD$?

A median of a triangle is $30$ cm long. How far is the centroid from the midpoint end of that median, in centimeters?

$G$ is the centroid of $\triangle ABC$ and $\overline{AD}$ is a median. If $AG = 4x + 4$ and $GD = x + 5$, what is $AD$?

Find the centroid of the triangle with vertices $(2, -1)$, $(8, 3)$ and $(-1, 7)$.

Find the orthocenter of the triangle with vertices $A(0, 0)$, $B(8, 0)$ and $C(6, 4)$.

Two sides of a triangle measure $7$ and $12$. How many whole-number lengths are possible for the third side?

In $\triangle XYZ$, $XY = 10$, $YZ = 15$ and $XZ = 8$. Which list orders the angles from smallest to largest?

In $\triangle ABC$ and $\triangle DEF$, $AB = DE$ and $AC = DF$. If $BC = 9$ and $EF = 12$, which statement must be true?