Question

extra credit #3: triangle midsegment

1. name all segments parallel to the given segment

a ( overline{yz}parallel )
b ( overline{rs}parallel )
c ( overline{xy}parallel )

Explanation:

Step1: Recall the triangle midsegment theorem

The triangle midsegment theorem states that a midsegment of a triangle is parallel to the third side of the triangle.

Step2: Identify midsegments and parallel sides for each part

• For part a: $\overline{YZ}$ is a midsegment. By the midsegment theorem, $\overline{YZ}\parallel\overline{RT}$
• For part b: $\overline{RS}$ is a side. The midsegment parallel to $\overline{RS}$ is $\overline{XZ}$ (since it connects the mid - points of the other two sides of the relevant sub - triangle)
• For part c: $\overline{XY}$ is a midsegment. By the midsegment theorem, $\overline{XY}\parallel\overline{TS}$

Answer:

a. $\overline{YZ}\parallel\overline{RT}$
b. $\overline{RS}\parallel\overline{XZ}$
c. $\overline{XY}\parallel\overline{TS}$