
629 F.3d 1083 (2011)
George Gerges RIZK; Nadia Youssef Attia; Joseph George Gerges; John George Gerges, Petitioners,
v.
Eric H. HOLDER, Jr., Attorney General, Respondent.
No. 06-74213.
United States Court of Appeals, Ninth Circuit.
Argued and Submitted September 2, 2010.
Filed January 3, 2011.
*1085 Ramsin Sheeno, Mansouri and Sheeno, Sherman Oaks, CA, attorney for the petitioners.
Daniel Glenn Lonergan, Office of Immigration Litigation, United States Department of Justice, Washington, DC, attorney for the respondent.
Before: DIARMUID F. O'SCANNLAIN, RONALD M. GOULD and SANDRA S. IKUTA, Circuit Judges.

OPINION
IKUTA, Circuit Judge:
George Gerges Rizk, the principal petitioner in this case, claims that the immigration judge (IJ) and Board of Immigration Appeals (BIA) erred in rejecting his asylum claim on the basis of an adverse credibility determination. Specifically, Rizk argues that he was not given a chance to explain the inconsistencies on which the IJ relied in finding him not credible. Because the record shows that Rizk did have ample opportunities to reconcile the numerous contradictions in his testimony, but failed to offer a reasonable and plausible explanation for them, the IJ's adverse credibility determination was supported by substantial evidence. We therefore deny his petition for review.

I
Rizk, a citizen of Egypt, entered the United States on December 6, 1998, as a nonimmigrant visitor for pleasure, with authority to remain in the United States until June 5, 1999. His wife, Nadia Youssef Attia (Attia), and two children, Joseph George Gerges (Joseph) and John George Gerges (John), entered the United States as nonimmigrant visitors on March 5, 1999, and were authorized to remain until September 4, 1999. In early 2000, all were issued Notices to Appear, charging them with being subject to removal under 8 U.S.C. § 1227(a)(1)(B) for having remained in the United States beyond the dates permitted by their visas. Rizk and his family conceded removability but sought relief in the form of asylum, withholding of removal, and relief under the Convention Against Torture (CAT). Rizk and his wife filed separate petitions for relief, and the children claimed derivative relief through each parent. See 8 C.F.R. § 207.7(a) (2010) (stating that a child accompanying an asylum applicant may share in the applicant's asylum status).
The IJ conducted an in-depth hearing over the course of three days. Rizk and Attia were the only witnesses, and each testified out of the hearing of the other. Their testimony focused on three separate incidents: the harassment and beating of their son Joseph for refusing to join in Islamic prayers, the break-in at the family's apartment, which led to Rizk's persecution by the police and prosecution for inciting sectarian chaos, and Attia's harassment by a Muslim, Mohammed Abdul Latif, culminating in her abduction and rape. For the reasons explained below, we focus mainly on the break-in incident.
The break-in and its aftermath are central to Rizk's claim of persecution. According to Rizk, on January 24, 1998, unknown perpetrators broke into the family's apartment, stole money and jewelry, and scrawled pro-Islamic slogans on the walls. After the police arrived to investigate, Attia accused Latif of committing the crime. *1086 The police took Rizk and Attia to the police station and interviewed them along with Latif. After preparing a report, the police detained Rizk overnight on the charge of "inciting sectarian chaos," allegedly because he accused a Muslim of breaking into and stealing from his apartment. The next day, the police transferred Rizk to State Security, where, Rizk asserted, he was interrogated, occasionally struck by officers, and given five minutes of electric shocks through his index fingers. He thereafter received letters requiring him to appear in court in connection with his prosecution on the incitement charge.
In a detailed, 37-page opinion, the IJ reviewed Rizk and Attia's testimony and detailed dozens of inconsistencies, including discrepancies as to times, dates, the sequence of events, and the identity of the individuals who participated in those events. The IJ pointed out internal inconsistencies, as well as inconsistencies between the stories offered by Rizk and Attia.[1] Most significantly, the petitioners' testimony contradicted the key piece of documentary evidence they had submitted: the police report on the break-in of their apartment. The IJ stated that "the unusual number of factual discrepancies present in the respondents' accounts, combined with the blatantly contradictory nature of those discrepancies, has left the respondents' representations dubious." In light of these numerous conflicts, the IJ determined that the petitioners were not credible, and indeed that their "testimony has left the Court in such disarray that it could not begin to discern the truth, if any, from the vast fallacies." Consequently, the IJ denied all of the petitioners' requested relief.
Following the IJ's rejection of their claims, petitioners appealed to the BIA. On December 29, 2003, the BIA "adopt[ed] and affirm[ed]" the IJ's opinion solely as to "the lead male respondent," i.e., Rizk. The BIA's opinion expressly did not address the appeals of Attia or the couple's children. Petitioners filed a timely petition for review of the BIA's decision.


*1087 II
On appeal, Attia argues that the BIA failed to address her challenge to the IJ's adverse credibility determination regarding her testimony. We agree. The BIA's opinion states: "The respondents consist of a married couple and their two children. For purposes of this order, reference to `the respondent' will refer to the lead male respondent." The opinion then upheld the IJ's adverse credibility as to the "respondent," and concluded that "the respondent's appeal is dismissed." In short, the BIA affirmed in full the IJ's decision as to Rizk, but did not mention Attia, John, or Joseph other than to include them in the definition of "respondents" (a term never again used in the opinion) and exclude them from the definition of "respondent."
At oral argument, the government asserted for the first time that the BIA did not address Attia's claims because they were not properly before it. According to the government, the petitioners' notice of appeal to the BIA addressed only Rizk's claims. Because Attia's claims were not exhausted, the government argues, we should dismiss her appeal for lack of jurisdiction. The record does not support this assertion. The petitioners' notice of appeal and supporting brief to the BIA lists the Alien Identification Number for each of the family members, repeatedly refers to the family collectively as "respondents" or "appellants," and refers specifically to the "female" appellant or respondent where appropriate. Accordingly, we conclude that Attia adequately appealed the IJ's decision and that we have jurisdiction over her petition.
Because the BIA's decision did not resolve Attia's appeal (and, consequently, did not resolve the cases of Joseph and John, who are eligible for derivative relief through Attia), we must grant her petition and remand her case (along with her children's) to the BIA for decision. "[W]here the BIA has not made a finding on an essential asylum issue, the proper course of action for a court of appeals is to remand the issue to the BIA for decision." Chen v. Ashcroft, 362 F.3d 611, 621 (9th Cir.2004) (citing INS v. Ventura, 537 U.S. 12, 17, 123 S.Ct. 353, 154 L.Ed.2d 272 (2002)). We therefore do not address Attia's additional challenges to the IJ's decision.

III
Rizk claims that the IJ's adverse credibility determination was not supported by substantial evidence. Where, as here, the BIA expressly adopts the IJ's decision, we review the IJ's findings as if they were the BIA's. Aguilar-Ramos v. Holder, 594 F.3d 701, 704 (9th Cir.2010). Because credibility determinations are findings of fact by the IJ, they "are conclusive unless any reasonable adjudicator would be compelled to conclude to the contrary." 8 U.S.C. § 1252(b)(4)(B) (2000). "To reverse [such a] finding we must find that the evidence not only supports [a contrary] conclusion, but compels it." INS v. Elias-Zacarias, 502 U.S. 478, 481 n. 1, 112 S.Ct. 812, 117 L.Ed.2d 38 (1992).
We must uphold the IJ's adverse credibility determination "[s]o long as one of the identified grounds is supported by substantial evidence and goes to the heart of[the alien's] claim of persecution." Wang v. INS, 352 F.3d 1250, 1259 (9th Cir.2003).[2] The IJ "must have *1088 a legitimate articulable basis to question the petitioner's credibility, and must offer a specific, cogent reason for any stated disbelief." Hartooni v. INS, 21 F.3d 336, 342 (9th Cir.1994); accord Singh v. Gonzales, 439 F.3d 1100, 1105 (9th Cir.2006). Major inconsistencies on issues material to the alien's claim of persecution constitute substantial evidence supporting an adverse credibility determination. See Kaur v. Gonzales, 418 F.3d 1061, 1064 (9th Cir.2005). This general rule has two qualifications, however. First, minor inconsistencies regarding non-material and trivial details, such as typographical errors or inconsistencies in specific dates and times that lack a close nexus to the petitioner's asserted grounds of persecution, cannot form the exclusive basis for an adverse credibility determination. Id. at 1064. Of course, even minor inconsistencies going to the heart of a petitioner's claim may, when considered collectively, "deprive [the] claim of the requisite `ring of truth,'" thereby supplying substantial evidence that will sustain the IJ's adverse credibility determination. Rivera v. Mukasey, 508 F.3d 1271, 1275 (9th Cir.2007) (quoting Kaur, 418 F.3d at 1067). Moreover, just as "repeated and significant inconsistencies" can deprive an alien's claim "of the requisite `ring of truth,'" so too can an inconsistency accompanied by "other indications of dishonestysuch as a pattern of clear and pervasive inconsistency or contradiction." Kaur, 418 F.3d at 1067.
Second, an IJ cannot base an adverse credibility determination on a contradiction that the alien could reconcile if given a chance to do so. Accordingly, the IJ must give the petitioner the opportunity to provide an explanation of an apparent inconsistency. Guo v. Ashcroft, 361 F.3d 1194, 1200 (9th Cir.2004). If the alien offers a "reasonable and plausible explanation" for the apparent discrepancy, the IJ must provide a specific and cogent reason for rejecting it. Soto-Olarte v. Holder, 555 F.3d 1089, 1091-92 (9th Cir.2009) (quoting Guo, 361 F.3d at 1201) (internal quotation marks omitted). If the IJ reasonably rejects the alien's explanation, see Osorio v. INS, 99 F.3d 928, 931 (9th Cir. 1996), or if the alien fails to provide a plausible explanation, the IJ may properly rely on the inconsistency as support for an adverse credibility determination. Kaur, 418 F.3d at 1065-67; see Guo, 361 F.3d at 1201. An IJ is not obliged to provide a protracted written or oral analysis of the alien's proffered explanation. Cf. Rita v. United States, 551 U.S. 338, 356-59, 127 S.Ct. 2456, 168 L.Ed.2d 203 (holding that the requirement of a reasoned decision in federal sentencing cases depends on the context of each individual case and that "[t]he appropriateness of brevity or length, conciseness or detail, when to write, what to say, depends on the circumstances"). Nor does the IJ have to engage in multiple iterations of the opportunity to explain. Once the IJ has provided a specific, cogent reason for disbelieving the alien's rationalization, the IJ need not offer the alien another opportunity to address the IJ's concerns, which the IJ would then need to address again. Moreover, the opportunity to explain may be provided through cross-examination by the government, see He v. Ashcroft, 328 F.3d 593, 602 (9th Cir.2003), or even direct examination by the alien's own attorney, see Rivera, 508 F.3d at 1275, not just through a colloquy between the alien and the IJ.

IV
Applying these principles, we begin by considering whether the factual discrepancies in Rizk's testimony constitute substantial evidence supporting the IJ's adverse credibility determination. Because we must uphold the IJ's adverse credibility determination so long as even one basis is supported by substantial evidence, *1089 Wang, 352 F.3d at 1259, we focus on one of the key contradictions the IJ identified: namely, the inconsistencies between the police report regarding the break-in and Rizk's testimony regarding the same incident.
Rizk originally introduced the police report as evidence of the break-in, and stated that "this report is[a] true and correct report." During the course of the hearing, however, questioning by the government and the IJ led to testimony that was directly inconsistent with the report on a range of key issues.
One discrepancy identified by the IJ related to a simple yet fundamental fact: the number of the apartment where Rizk lived and the break-in took place. In his testimony, Rizk stated his family's apartment number was 14. However, the police report stated that the break-in was in apartment 8. The government asked the following:
Q. Does this police report relate to the robbery or the breaking in of your apartment?
A. Yes.
Q. The police report says that the apartment that was broken into was apartment number eight. Is that the wrong apartment?
A. The building  each floor consists of, the building is seven story building and each story has two apartments, 14 by eight.
The IJ then added a question:
Q. So, the apartment that you and your wife lived in with your family was apartment 14.
A. Yes. Maybe there is a mistake in the translation. I don't know.
A second discrepancy involved the identity of the person who first discovered the break-in. Rizk claimed that Attia discovered the break-in while Joseph was still in school, and that Rizk ran back to the apartment and called the police. The government asked Rizk to explain why the police report stated that Joseph discovered the break-in.
Q. Did your son Joseph come into the apartment while the police were there investigating the break in?
A. No, he was not back.
Q. According to the police report, it says that you were not there when the police arrived but that the son of the owner, Joseph George Rizk, 15 years old, had come in. Is this inaccurate?
A. I don't recall.
Q. Well, was Joseph at the apartment when you got home?
A. I don't recall if, I don't recall if he was there because when I arrived, I ran to check the apartment. I don't recall whether he was there or not.
Further, the police report said that Mr. Mohamed Said Abraham first reported the robbery of Rizk's apartment to the police. On questioning, Rizk denied that this was correct.
Q. Is Mohamed Said Abraham (phonetic sp.) a neighbor?
A. No, we don't know this person. We just found his name in the report.
Q. You testified you yourself called the police. Is that correct?
. . .
A. Yes, and I don't know why they write it like this. I was the one who called the police.
A third discrepancy involved whether Rizk and Attia had told the police that Latif was the perpetrator of the break-in. This accusation of Latif was central to Rizk's claim of persecution, because it allegedly triggered the subsequent police harassment and prosecution for inciting sectarian chaos. The police report stated that the couple had not made any accusation against Latif, or indeed any accusation at all. In light of this crucial inconsistency, *1090 the government made the following inquiry:
Q. According to the police report, you were asked whether you accused of anyone and you replied no. Was this incorrect?
A. This is a fake report. How would they give me a report saying that I accused a Muslim person?
Q. Well, sir, if this is a fake report, why are you offering it to this Court?
A. This is the report that they gave me but they haven't told the truth in the report. Of course, they're not going to write in that report that a Muslim person broke into an apartment and wrote on the walls there is no God but one God. They won't do that.
Q. Sir, you testified that you fear going back to Egypt because of a case where you accused a Muslim person of breaking into your apartment. Yet, the document you brought to us makes no reference to any Muslim person or anyone for that matter breaking into your apartment.
A. As I told you before, they're not going to mention that in the report. How would they mention that a Muslim person had broken into the apartment[?]
Q. So, where is this record that you accused a Muslim person?
A. The report is with them and they're not going to give it to me. These are all fabricated.
The IJ similarly asked:
Q. That report goes on to state that there was absolutely, there was no allegation against anyone from plaintiff. Our investigation did not lead us to any suspect. This is the report from the police department. This is a document that you submitted. Why do you think that this document would explicitly state that you did not bring any allegations against anyone and that there was no suspect?
A. Things like this, they don't mention it in the reports. They're not going to mention it in the reports. He was supposed to say that the apartment was vandalized and the pictures were thrown on the floor. Why didn't he mention that?
In light of these and other passages in the record, it is clear that Rizk had ample opportunity to explain the reasons for inconsistencies in the record, but failed to offer plausible explanations. Instead, Rizk attempted to evade questions by claiming a failure of memory, or by speculating that the police intentionally falsified the report and that there were mistakes in the translation. These excuses themselves contradict Rizk's earlier testimony that the police report is a "true and correct report." Rizk's claim that the police intentionally omitted his accusation against Latif is particularly implausible, given Rizk's further claim that the police harassed him and the government prosecuted him for making this very accusation. The IJ pointed out and discussed these inconsistencies at length. Regarding the break-in, the IJ stated:
[T]he crux of the respondents' account lies in the circumstances of the alleged January 24, 1998 break-in at their apartment. This was a particularly violent event in which their home was allegedly vandalized, their belongings were broken, their valuables stolen, and it precipitated the four day incarceration and alleged torture of the male respondent. However, despite the significance of this day and all of the events which came to pass during it, the respondents could not describe it clearly or consistently.
Regarding the police report, she said: "[V]arious aspects of the [petitioners'] account are entirely implausible. Despite the fact that corroboration is generally not required, the respondents elected to submit *1091 the police report detailing their breakin... into the record." The IJ then recited the discrepancies described above, and concluded: "When afforded abundant opportunities to explain their misstatements during their many hours of testimony, the [petitioners] typically elected to dredge themselves deeper into this murky mess from which they cannot recover, ... undermining any shred of credibility at all then remaining." In light of these inconsistencies and the implausibility of the petitioners' accounts, the IJ found the petitioners not credible, declaring that she "[wa]s not in a position to believe any of the information provided by the respondents regarding their alleged past persecution in Egypt."
Because Rizk did not offer a reasonable and plausible explanation for the discrepancies, which went to the heart of his claim, either individually or in the aggregate, even though he had ample opportunity to do so, the contradictions on which the IJ relied remain substantial evidence supporting the IJ's adverse credibility determination. No express, point-by-point rejection of Rizk's explanations was necessary. See Rivera, 508 F.3d at 1275; Kaur, 418 F.3d at 1065-67; see Soto-Olarte, 555 F.3d at 1091, 1094-95.
Because we cannot say that "any reasonable adjudicator would be compelled to conclude" that Rizk is credible, 8 U.S.C. § 1252(b)(4)(B) (2000); accord Elias-Zacarias, 502 U.S. at 481 n. 1, 112 S.Ct. 812, we uphold the IJ's adverse credibility determination. In the absence of his discredited testimony, Rizk cannot meet his burden of establishing past persecution or a well-founded fear of future persecution on a protected ground, and we therefore also uphold the IJ's determination that Rizk is not eligible for asylum.[3]

V
For the foregoing reasons, we DENY the petition for review as to Rizk. As to Attia, John, and Joseph, we GRANT the petition and REMAND to the BIA so that it may address their appeal from the IJ's September 26, 2001 order denying relief from removal.[4]
DENIED IN PART; GRANTED AND REMANDED IN PART.
NOTES
[1]  It is difficult to convey the full extent of the inconsistencies that pervade the petitioners' testimony. For present purposes, we can provide only a small sample of the many discrepancies apparent in the record. For example, Rizk reported that Attia called him immediately upon discovering the break-in, around 2:00 or 2:30 p.m. and that he went home directly and called the police. But the IJ noted that Rizk first stated he called the police at 2:30 p.m., and then stated he called the police at 4:00 p.m., while Attia stated that Rizk called the police at 2:00 p.m. Rizk subsequently stated that the police arrived between 4:00 and 4:30 in the afternoon, while Attia testified that they came around 2:10 p.m. At another juncture, Rizk stated that Attia obtained the police report submitted in the immigration proceedings with the help of individuals "inside" the police department, while Attia said that one of Rizk's brothers, Magdi, procured the report.

On the subject of the letters sent by the court to Rizk in connection with prosecution for incitement of sectarian chaos, Rizk first claimed he received no letters while in Egypt, but then said he received three letters in November 1998 (before leaving for the United States). Attia, however, said that he received four letters: three in July 1998 and one in September 1998.
Attia's and Rizk's accounts also disagreed on the chronology of Latif's alleged harassment of Attia. According to Rizk, Latif began accosting Attia in summer 1997, and his last attempt to convince her to convert to Islam was sometime between August 1997 and December 1997. Specifically, Rizk testified as follows about the last date of Latif's harassment: "Maybe it was October, end of November or beginning of December. Beginning of November or end of November, end of October, beginning of November." Attia stated that she did not meet Latif until January 2, 1998, however, which was after the last date indicated in Rizk's account.
[2]  Although the REAL ID Act of 2005, Pub.L. No. 109-13, Div. B, Title I, § 101(h)(2), 119 Stat. 231, has modified the scope of our review of an IJ's adverse credibility finding for asylum applications filed after May 11, 2005, these modifications are not applicable here because Rizk filed his application before the REAL ID Act's effective date.
[3]  Rizk also argued that his rights to due process and equal protection were violated because the BIA relied on the IJ's flawed decision. Because we determine that the IJ's adverse credibility determination was supported by substantial evidence, we reject this argument. Moreover, because Rizk did not raise his withholding-of-removal and CAT claim in his opening brief, we deem those issues waived. Martinez-Serrano v. INS, 94 F.3d 1256, 1259 (9th Cir. 1996); see Fed. R.App. P. 28(a)(9)(A).
[4]  Each party shall bear its own costs.
