{"id":"cb_question_bank:2c4ce1d4-fff0-4905-979e-6bd2f82a8fbc","source_id":"cb_question_bank","source_item_id":"2c4ce1d4-fff0-4905-979e-6bd2f82a8fbc","external_id":"ce3b6f4f-60f0-4503-b733-4d7804f8a14b","ibn":null,"question_id":"901c3215","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.B.","skill":"Lines, angles, and triangles","difficulty":"H","score_band":7,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"In triangles upper A upper B upper C and upper D upper E upper F , angles upper B and upper E each have measure 27 degree and angles upper C and upper F each have measure 41 degree . Which additional piece of information is sufficient to determine whether triangle upper A upper B upper C is congruent to triangle upper D upper E upper F ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">In triangles <math alttext=\"upper A upper B upper C\"><mrow>\n\t<mi>A</mi>\n\t<mi>B</mi>\n\t<mi>C</mi>\n</mrow>\n</math> and <math alttext=\"upper D upper E upper F\"><mrow>\n\t<mi>D</mi>\n\t<mi>E</mi>\n\t<mi>F</mi>\n</mrow>\n</math>, angles <math alttext=\"upper B\"><mi>B</mi>\n</math> and <math alttext=\"upper E\"><mi>E</mi>\n</math> each have measure <math alttext=\"27 degree\"><mrow><mn>27</mn></mrow><mo>°</mo></math> and angles <math alttext=\"upper C\"><mi>C</mi>\n</math> and <math alttext=\"upper F\"><mi>F</mi>\n</math> each have measure <math alttext=\"41 degree\"><mrow><mn>41</mn></mrow><mo>°</mo></math>. Which additional piece of information is sufficient to determine whether triangle <math alttext=\"upper A upper B upper C\"><mrow>\n\t<mi>A</mi>\n\t<mi>B</mi>\n\t<mi>C</mi>\n</mrow>\n</math> is congruent to triangle <math alttext=\"upper D upper E upper F\"><mrow>\n\t<mi>D</mi>\n\t<mi>E</mi>\n\t<mi>F</mi>\n</mrow>\n</math>?</p>","rationale_html":"<p style=\"text-align: left;\">Choice C is correct. Since angles <math alttext=\"upper B\"><mi>B</mi>\n</math> and <math alttext=\"upper E\"><mi>E</mi>\n</math> each have the same measure and angles <math alttext=\"upper C\"><mi>C</mi>\n</math> and <math alttext=\"upper F\"><mi>F</mi>\n</math> each have the same measure, triangles <math alttext=\"upper A upper B upper C\"><mrow>\n\t<mi>A</mi>\n\t<mi>B</mi>\n\t<mi>C</mi>\n</mrow>\n</math> and <math alttext=\"upper D upper E upper F\"><mrow>\n\t<mi>D</mi>\n\t<mi>E</mi>\n\t<mi>F</mi>\n</mrow>\n</math> are similar, where side <math alttext=\"upper B upper C\"><mrow>\n\t<mi>B</mi>\n\t<mi>C</mi>\n</mrow>\n</math> corresponds to side <math alttext=\"upper E upper F\"><mrow>\n\t<mi>E</mi>\n\t<mi>F</mi>\n</mrow>\n</math>. To determine whether two similar triangles are congruent, it is sufficient to determine whether one pair of corresponding sides are congruent. Therefore, to determine whether triangles <math alttext=\"upper A upper B upper C\"><mrow>\n\t<mi>A</mi>\n\t<mi>B</mi>\n\t<mi>C</mi>\n</mrow>\n</math> and <math alttext=\"upper D upper E upper F\"><mrow>\n\t<mi>D</mi>\n\t<mi>E</mi>\n\t<mi>F</mi>\n</mrow>\n</math> are congruent, it is sufficient to determine whether sides <math alttext=\"upper B upper C\"><mrow>\n\t<mi>B</mi>\n\t<mi>C</mi>\n</mrow>\n</math> and <math alttext=\"upper E upper F\"><mrow>\n\t<mi>E</mi>\n\t<mi>F</mi>\n</mrow>\n</math> have equal length. Thus, the lengths of <math alttext=\"upper B upper C\"><mrow>\n\t<mi>B</mi>\n\t<mi>C</mi>\n</mrow>\n</math> and <math alttext=\"upper E upper F\"><mrow>\n\t<mi>E</mi>\n\t<mi>F</mi>\n</mrow>\n</math> are sufficient to determine whether triangle <math alttext=\"upper A upper B upper C\"><mrow>\n\t<mi>A</mi>\n\t<mi>B</mi>\n\t<mi>C</mi>\n</mrow>\n</math> is congruent to triangle <math alttext=\"upper D upper E upper F\"><mrow>\n\t<mi>D</mi>\n\t<mi>E</mi>\n\t<mi>F</mi>\n</mrow>\n</math>.</p>\n<p style=\"text-align: left;\">Choice A is incorrect and may result from conceptual errors.</p>\n<p style=\"text-align: left;\">Choice B is incorrect and may result from conceptual errors.</p>\n<p style=\"text-align: left;\">Choice D is incorrect. The given information is sufficient to determine that triangles <math alttext=\"upper A upper B upper C\"><mrow>\n\t<mi>A</mi>\n\t<mi>B</mi>\n\t<mi>C</mi>\n</mrow>\n</math> and <math alttext=\"upper D upper E upper F\"><mrow>\n\t<mi>D</mi>\n\t<mi>E</mi>\n\t<mi>F</mi>\n</mrow>\n</math> are similar, but not whether they are congruent.</p>","correct_answer":["C"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.838000+00:00","source_updated_at":"2023-08-02T20:25:59.838000+00:00","options":[{"label":"A","content_html":"<p style=\"text-align: left;\">The measure of angle <math alttext=\"upper A\"><mi>A</mi>\n</math></p>","ord":0},{"label":"B","content_html":"<p style=\"text-align: left;\">The length of side <math alttext=\"upper A upper B\"><mrow>\n\t<mi>A</mi>\n\t<mi>B</mi>\n</mrow>\n</math></p>","ord":1},{"label":"C","content_html":"<p style=\"text-align: left;\">The lengths of sides <math alttext=\"upper B upper C\"><mrow>\n\t<mi>B</mi>\n\t<mi>C</mi>\n</mrow>\n</math> and <math alttext=\"upper E upper F\"><mrow>\n\t<mi>E</mi>\n\t<mi>F</mi>\n</mrow>\n</math></p>","ord":2},{"label":"D","content_html":"<p style=\"text-align: left;\">No additional information is necessary.</p>","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}