Identify the option that correctly uses a homonym of the bolded term:

The infantrymen were trained to march with a long pike in tight rows.

The correct option is: "While fishing near the lake shore, he caught a large pike."

A homonym refers to a word that shares the same spelling and pronunciation as another word, but has a completely different meaning and origin.

In the given sentence, "The infantrymen were trained to march with a long pike in tight rows", the word pike refers to a historical weapon—a long wooden shaft with a pointed steel head.

Let us analyze each option:

1. "Each soldier carried a sturdy pike to defend against incoming cavalry."
Here, "pike" refers to the weapon. This is the same meaning as the original sentence, not a homonym usage.

2. "The guard held a heavy pike while standing watch at the castle gates."
Here, "pike" also refers to the weapon. This uses the same meaning as the original sentence.

3. "While fishing near the lake shore, he caught a large pike."
Here, "pike" refers to a species of large, predatory freshwater fish. Since this word has the exact same spelling and sound but a completely different meaning (a fish vs. a weapon), it correctly uses a homonym of the bolded term.

4. "The medieval weapon featured a sharp iron tip mounted on a long wooden pole."
This sentence describes the weapon itself and does not use the word "pike".

Therefore, the third option correctly uses a homonym of the term pike.