Use $\triangle G H J$, where D, E, and F are midpoints of the sides.

If HJ=8x-2 and DF=2x+11, what is HJ?

In the given diagram, the perpendicular bisectors of $\triangle A B C$ meet at point G and are shown dashed. Find CF.

Is it possible to construct a triangle with the given side lengths such 17, 17, and 33? If not, explain why not.

Copy and complete the statement for $\triangle H J K$ with medians $\overline{H N}, \overline{J L}$, and $\overline{\boldsymbol{K} \boldsymbol{M}}$, and centroid P.

PN= $\underline{~~?~~}$ HN

Use $\triangle G H J$, where D, E, and F are midpoints of the sides.

If EF=2x+7 and GH=5x-1, what is EF?

Arrange statements A-F in order to write an indirect proof of Case 1.

GIVEN: $\overline{A D}$ is a median of $\triangle A B C$. $\angle A D B \cong \angle A D C$

PROVE: $A B=A C$

Case 1:

A. Then $m \angle A D B<m \angle A D C$ by the converse of the Hinge Theorem.

B. Then $\overline{B D} \cong \overline{C D}$ by the definition of midpoint. Also, $\overline{A D} \cong \overline{A D}$ by the reflexive property.

C. This contradiction shows that the temporary assumption that AB<AC is false.

D. But this contradicts the given statement that $\angle A D B \cong \angle A D C$.

E. Because $\overline{A D}$ is a median of $\triangle A B C, D$ is the midpoint of $\overline{B C}$.

F. Temporarily assume that AB<AC.

Is it possible to construct a triangle with the given side lengths such 1, 4, and 6? If not, explain why not.

Find the indicated measure.

Point P is the incenter of $\triangle H K M$. Find BG. Find JP.

Find the measurements.

Given that G is the centroid of $\triangle A B C$, find FG and BD.

One contestant in a catch-and-release fishing contest spends the morning at a location 1.8 miles due north of the starting point, then goes 1.2 miles due east for the rest of the day. A second contestant starts out 1.2 miles due east of the starting point, then goes another 1.8 miles in a direction 84$^{\circ}$ south of due east to spend the rest of the day. Which angler is farther from the starting point at the end of the day? Explain how you know.

In the given diagram, the perpendicular bisectors of $\triangle A B C$ meet at point G and are shown dashed. Find BD.

Use $\triangle G H J$, where D, E, and F are midpoints of the sides.

If DE=4x+5 and GJ=3x+25, what is DE?

In the given diagram, the perpendicular bisectors of $\triangle A B C$ meet at point G and are shown dashed. Find AG.

Find the measurements.

Given that AB=BC, find AD and $m \angle A B C$.