Question

nl = \\_\\_\\_\\_\\_\\_

Explanation:

Identify given geometric markings

Using the Triangle Congruence knowledge point

• The angle at vertex \(J\) has a single arc with a tick mark, and the angle at vertex \(N\) has a single arc with a tick mark, indicating \(\angle J \cong \angle N\).
• The segment \(JL\) has a length corresponding to \(NL\) if the triangles are congruent, but let's look at the intersection at \(L\). The lines \(JM\) and the vertical segment intersect at \(L\).
• This intersection creates vertical angles: \(\angle JL(\text{top}) \cong \angle MLN\). Let the top vertex be \(K\). Thus, \(\angle KLJ \cong \angle MLN\) by the Vertical Angles theorem.
• The markings show \(\angle J \cong \angle N\).
• The tick marks on the segments: segment \(JK\) and segment \(NM\) do not have explicit tick marks, but the segments \(JL\) and \(NL\) are positioned such that \(L\) is the midpoint, or the tick marks on the angles indicate \(\angle KJL \cong \angle MNL\).
• Let's identify the corresponding parts for the congruence statement. The triangles are \(\triangle KJL\) and \(\triangle MNL\).
• By CPCTC (CPCTC), corresponding segments are equal. Therefore, the segment corresponding to \(NL\) is \(JL\).

Determine the corresponding segment

Using the CPCTC knowledge point

• In the congruence correspondence \(\triangle KJL \cong \triangle MNL\):
• Vertex \(J\) corresponds to vertex \(N\).
• Vertex \(L\) corresponds to vertex \(L\).
• Vertex \(K\) corresponds to vertex \(M\).
• Therefore, the segment \(NL\) corresponds directly to the segment \(JL\).

Answer:

\(NL =\) <blank>\(JL\)</blank>