Gezirah shavah [#2 Ishmael, #7 Eliezer]
Gezirah Shavah [equivalent expressions or argument by analogy] is a hermeneutic rule that allows us to understand aspects of a particular command when certain details are left unspecified. Since Gezirah means, law, [see Daniel 4:14] the principle is used to compare two similar laws. For instance, we were to slaughter the Pesach Lamb b’moado, in its appointed time [Numbers 9:2]. This same term is used in Numbers 28:2 in reference to the Tamid offering, which is offered on Shabbat as well. Therefore, a Gezirah Shavah permits us to understand that the Pesach lamb is slaughtered even on Shabbat! [The lack of a Gezirah Shavah tells us we do not blow the shofar when Rosh Hashanah lands on Shabbat.] In this example, the Tamid becomes the “parent mitzvah” and the Pesach offering the “orphaned mitzvah,” orphaned, because it needs the Tamid offering to define “at its appointed time.”
We are able to create a comparison between 1 Samuel 1:11 and Judges 13:5, using the term, lo yaaleh al rosho, which is translated as shall not go upon his head. At first blush, one would say that the torah of nazirus [found in Numbers 6:1-21] is all we need to figure out that the children in question are nazir, but that may not be the case. There are other cases in Torah where one shaves the head [cf. Genesis 41:14, Leviticus 13:33, 14:8-9]. Therefore, the gezirah shavah existing between Judges 13:5 [the parent] and 1 Samuel 1:11 [the orphan] – and not the passage found in Numbers 6:1-21 – provides additional information to answer that both young lads are nazir from birth.
Another example is found in Leviticus 1:15 and 5:8, where the phrase, umlak et rosho [wring off the head] occurs. The phrase is found nowhere else in Torah. In Leviticus 1:15, the passage states, “The priest shall… …nip off its head, etc.” In 5:8, the passage states, “And he shall nip off his head from his neck, etc.” The gezirah shavah uses the passage with additional information [15:8] to expound upon the passage with lesser information [1:15]. Therefore, we know that in both cases, the Priest uses his nail at the base of the head [presumably severing the spinal column from the pons, which is right under the cerebellum] to pinch the head off the neck of the bird, leaving the neck attached.
Because of the possibility of abuse, the command was restricted. According to Talmud [b.Pesachim 66a, b.Bava Kamma 2b, Chagigah 10b, and b.Niddah 19b, 22b-23a], one does not have the permission to advance a gezirah shavah independently; he must receive the tradition from his teachers. Additionally, the verses both must be from the Torah and they must not only be similar but mufneh [superfluous or free] within the context in which they appear. If it cannot be argued that the text was placed there for the express purpose of a gezirah shavah, it is not an irrefutable gezirah shavah [b.Shabbat 64a 131a, b.Yevamot 70b 74a, b.Bava Kamma 25b, b.Niddah 22b-23a]. R’ Akiva states, however, that the superfluous requirement is unnecessary [y.Yoma 8:3]. Yerushalmi states, “From a gezirah shavah, conclusions may be deduced to support tradition, but not such that oppose tradition.” However, a Gezirah Shavah that is not mufneh on both sides can be refuted if  one side of mufneh and the other side teaches something superior (for a stringency) or deficient (for a leniency),  it is not successfully contested.
An example for a non-authorized gezirah shavah exists in Parashah Vayelech. Deuteronomy 31:3 uses the term, “hu over lefanecha” [cross over before you] for both Hashem and for Joshua. Certainly this doesn’t mean Joshua is Hashem! Heaven forbid! This example is a false gezirah shavah for three reasons: It produces a ridiculous result, it’s not a tradition passed down from our Rabbis, and it is not finding equivalence between two laws.
There is a hermeneutic principle called hechesh [comparison]. This is very limited, in that it applies to two laws within the same verse. “You shall not eat leavened bread with it; for seven days you shall eat matzot because of it” [Deuteronomy 16:3]. With two laws sharing equivalence in the same verse [the positive mitzvah of eating unleavened with the negative mitzvah of not eating leavened], hechesh says that while women are exempt from carrying out positive commands based upon time, this verse structure indicates that women are NOT exempt from NOT eating leavening. [cf. b.Pesachim 43b].
Semuchim, another similar principle, refers to the juxtaposition of two laws in two adjacent verses. For instance, Exodus 22:17 says we’re not to let a sorceress to live. Verse 18 states that people who have sex with animals are to be stoned to death. Semuchim rules that just as the one who lies with a beast is stoned to death, so to a sorcerer is to be stoned to death [cf. b.Berachot 21b]. R’Judah states semuchim applies ONLY to Deuteronomy.