Special Segments in Triangles (Set 2) Worksheet

Sample problems

A median joins a vertex to the midpoint of the opposite side; the three medians meet at the centroid, which divides each median in a $2:1$ ratio (the longer part is from the vertex). An altitude is perpendicular to a side. A perpendicular bisector passes through a side's midpoint at a right angle; points on it are equidistant from the side's endpoints. An angle bisector splits an angle into two equal halves. A midsegment joins two midpoints, is parallel to the third side, and is half its length.

1. 1. A midsegment of a triangle is parallel to the third side and is half its length. If the third side has length $30$, find the length of the midsegment.
2. 2. A midsegment of a triangle has length $11$. Find the length of the side it is parallel to.
3. 3. In a triangle, $G$ is the centroid and $\overline{AM}$ is a median with $M$ on the opposite side. If the part from the vertex $AG=14$, find $GM$ and the full median $AM$.
4. 4. A median of a triangle has total length $30$. Its centroid divides it in a $2:1$ ratio. Find the distance from the vertex to the centroid.

Plus 10 more problems and a full answer key in the PDF.