Question

use the image to answer the question image long description based on the construction shown in the diagram, complete the statements with the correct symbol. l □ xy xp □ py

Explanation:

Step1: Analyze the angle between line \( l \) and \( \overline{XY} \)

From the diagram, there is a right - angle symbol at point \( P \) between line \( l \) and segment \( \overline{XY} \). When two lines (or a line and a segment) form a right angle (90 degrees) between them, they are perpendicular. The symbol for perpendicular is \( \perp \). So, \( l\perp\overline{XY} \).

Step2: Analyze the lengths of \( XP \) and \( PY \)

Since the construction (the arcs and the perpendicular lines) suggests that \( P \) is the mid - point of \( \overline{XY} \) (because the perpendicular from the line \( l \) to \( \overline{XY} \) bisects \( \overline{XY} \) in such a construction), the length of \( XP \) is equal to the length of \( PY \). The symbol for equality of lengths (or segments) is \( = \). So, \( XP = PY \).

Answer:

For \( l\square\overline{XY} \), the symbol is \( \perp \); for \( XP\square PY \), the symbol is \( = \).