Identify parallel and perpendicular lines from the provided graph, showing your reasoning.

Here are the parallel and perpendicular lines identified from the graph:

Parallel Lines:

• $\overline{AB} \parallel \overline{PQ}$
• $\overline{AB} \parallel \overline{UV}$
• $\overline{AB} \parallel \overline{MN}$
• $\overline{PQ} \parallel \overline{UV}$
• $\overline{PQ} \parallel \overline{MN}$
• $\overline{UV} \parallel \overline{MN}$
• $\overline{ST} \parallel \overline{GH}$

Perpendicular Lines:

• $\overline{UV} \perp \overline{XY}$ (Vertical line $\overline{UV}$ intersects horizontal line $\overline{XY}$ at point X, forming a $90^\circ$ angle.)
• $\overline{ST} \perp \overline{EF}$ (Line $\overline{ST}$ has a slope of 1, and line $\overline{EF}$ has a slope of $-1$. Since the product of their slopes is $-1$, they are perpendicular.)
• $\overline{GH} \perp \overline{EF}$ (Line $\overline{GH}$ has a slope of 1, and line $\overline{EF}$ has a slope of $-1$. Since the product of their slopes is $-1$, they are perpendicular.)