Geometry / Unit 6: Relationships in Triangles
6.1 Midsegments of Triangles
Notes
A midsegment joins the midpoints of two sides of a triangle.
- Triangle Midsegment Theorem: a midsegment is parallel to the third side and half as long.
- Every triangle has three midsegments. They form a smaller triangle with half the perimeter.
- Example: in $\triangle ABC$, $D$ and $E$ are midpoints of $\overline{AB}$ and $\overline{AC}$. If $BC = 18$, then $DE = 9$ and $\overline{DE} \parallel \overline{BC}$.
Practice
$\overline{MN}$ is a midsegment of $\triangle PQR$ parallel to $\overline{QR}$. If $QR = 22$, what is $MN$?
A midsegment is half the length of the third side.
$\overline{DE}$ is a midsegment of $\triangle ABC$ parallel to $\overline{BC}$. $DE = 2x + 1$ and $BC = 5x - 4$. Find $BC$.
$2(2x + 1) = 5x - 4$, so $4x + 2 = 5x - 4$ and $x = 6$. $BC = 26$.
A triangle has sides 10, 14 and 18. What is the perimeter of the triangle formed by its three midsegments?
Each midsegment is half a side: $5 + 7 + 9 = 21$.
Ready for more? Take the Unit 6 test.