Sarah is Abraham's sister?

Question

Genesis 20:12 has Abraham honestly saying that Sarah is indeed his sister when he is talking with Abimelek.

Besides, she really is my sister, the daughter of my father though not of my mother; and she became my wife.

How is this compatible with Genesis 11:31 which describes Sarah as being merely Terach's daughter -in-law, rather than as his daughter (a more immediate relationship, and therefore presumably more worthy of mention)?

Terah took his son Abram, his grandson Lot son of Haran, and his daughter-in-law Sarai, the wife of his son Abram, and together they set out from Ur of the Chaldeans to go to Canaan. But when they came to Harran, they settled there.

Answer 1

There is a Midrash (Megillah 14a) that Sarah was really the same as Yiskah (from Gen 11:28), which would make her Avraham's niece, which is pretty close to a sister.

However, Ibn Ezra (Gen 20:12) writes that Avraham was just saying something to appease Avimelekh, and we shouldn't assume it is true. Indeed he addresses your question earlier (Gen 11:28) when he writes that were Sarah the same as Yiskah, your verse should have specified "his granddaughter" as it did with Yiskah's sibling Lot (and mutatis mutandis were Sarah actually Avaraham's half-sister).

This actually has a Halakhic application, as the Talmud (Sanhedrin 58b) in discussing whether or not the Noahide rules of incest apply to a maternal half-sibling cites Gen 20:12 to show that Avraham was being careful to avoid concerns of incest. This would only make sense if Sarah was not the same as Yiskah (as there is no prohibition of incest with a niece, even for Jews). While the Talmud rejects the proof due to the aforementioned Midrash, the Rambam (Melakhim 9:5) rules in accordance with the proof, citing the verse explicitly in his code. Rav Yosef Karo in his commentary there says this is due to its being פשטיה דקרא the simple reading of the verse, while the Midrashic answer is שינויא דחיקא a forced change.

In short: there is a Midrash that they were indeed related somehow, but we are left with your question among others, and the simple reading is that Avraham was just trying to placate Avimelekh and wasn't related to Sarah at all.

Answer 2

Rashi on Genesis 20:12 points out that she was actually Haran's daughter and thereby the granddaughter of Terach. To explain the fact that she is called Abraham's half-sister, he employs the Talmudic principle of בני בנים הרי הם כבנים, that grandchildren are considered as children. Therefore, Sarah was truly Avraham's sister in the sense that she was his half-sister (although in reality his niece), yet she is also referred to later as Terach's daughter-in-law since that is indeed what she was to him in relation to Avraham.

Answer 3

Sara was the daughter of Haran (Avraham's brother), the sister of Lot and was also called Yiskah. In order to keep the women in the family, Avram and Nachor married the two daughters of their brother Haran.

Bereishis 11:29

29 And Abram and Nahor took themselves wives; the name of Abram's wife was Sarai, and the name of Nahor's wife was Milcah, the daughter of Haran, the father of Milcah and the father of Iscah.

Rashi

Iscah: This is Sarah [called Iscah] because she would see (סוֹכָה) through Divine inspiration, and because all gazed (סוֹכִין) at her beauty. Alternatively, יִסְכָּה is an expression denoting princedom, (נְסִיכוּת), just as Sarah is an expression of dominion (שְׂרָרָה) . - [from Meg. 14a]

That is why Rashi in 20:12 says

my sister, the daughter of my father: And the daughter of one’s father is permitted to a Noahide [for marriage], for a gentile has no father (i.e., his lineage is not traced from his father). And in order to justify his words, he answered him in this way. Now if you ask: Was she not the daughter of his brother? [The answer is that] grandchildren are considered like children (Tosefta, Yev. 8:8; Talmud Bavli, Yev. 62b); therefore, she was (considered as) Terah’s daughter. And so did he say to Lot, “For we are kinsmen” (אֲנָשִׁים אַחִים) [lit. men, brothers] (although, in fact, Lot was his brother Haran’s son). - [from Pirkei d’Rabbi Eliezer, ch. 36]

but not the daughter of my mother: Haran was [born] of a different mother [than Abraham]. —