Question

1. name the segment parallel to the given segment.

a) $overline{yz}$ || ______
b) $overline{rs}$ || ______
c) $overline{xy}$ || ______

Explanation:

Step1: Use the mid - segment theorem

The mid - segment theorem states that the segment connecting the mid - points of two sides of a triangle is parallel to the third side.
For part (a), since \(X\) is the mid - point of \(RT\) and \(Z\) is the mid - point of \(ST\), by the mid - segment theorem, \(\overline{YZ}\parallel\overline{XT}\).

Step2: Analyze the parallel relationship

For part (b), we can observe the figure. If we consider the quadrilateral formed in a certain way (by using the properties of mid - points and line segments). We know that \(\overline{RS}\parallel\overline{XZ}\) (by the mid - segment theorem or the property of parallel lines in a geometric figure with mid - point connections).

Step3: Apply the mid - segment theorem again

For part (c), since \(Y\) is the mid - point of \(RS\) and \(X\) is the mid - point of \(RT\), by the mid - segment theorem, \(\overline{XY}\parallel\overline{SZ}\).

Answer:

a) \(\overline{XT}\)
b) \(\overline{XZ}\)
c) \(\overline{SZ}\)