Alternate Angles X and Y: True or False in Parallel Lines AB || CD

To determine if $X$ and $Y$ are alternate angles, let's first identify the necessary components of the diagram:

• Lines $AB$ and $CD$ are parallel, stated by $AB \parallel CD$.
• There is a transversal intersecting both parallel lines $AB$ and $CD$.
• Angles $X$ and $Y$ are formed by this intersection.

According to the alternate interior angles theorem, when a transversal crosses two parallel lines, each pair of alternate interior angles is equal. Alternate angles appear on opposite sides of the transversal and between the two lines.

In the given diagram:
- Angle $X$ appears below point $B$ where the transversal intersects $AB$.
- Angle $Y$ appears above point $C$ where the transversal intersects $CD$.
These angles are formed on opposite sides of the transversal and between the lines $AB$ and $CD$, fulfilling the condition for alternate angles.

Therefore, $X$ and $Y$ are indeed alternate angles according to the given conditions.

The conclusion is that the statement "X and Y are alternate angles" is True.