{"id":"cb_question_bank:965d002f-8928-4cb5-8474-6a31d1ce273d","source_id":"cb_question_bank","source_item_id":"965d002f-8928-4cb5-8474-6a31d1ce273d","external_id":null,"ibn":"027209-DC","question_id":"1c3d613c","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.B.","skill":"Lines, angles, and triangles","difficulty":"M","score_band":4,"answer_type":"spr","answer_source":"rationale","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Triangle ABC and triangle DEF are shown. The relationship between the side lengths of the two triangles is such that the length of side A, B, over, the length of side D E, equals, the length of side B C, over, the length of side E F, which equals, the length of side A, C, over, the length of side D F, which equals 3 . If the measure of angle BAC is 20°, what is the measure, in degrees, of angle EDF ? (Disregard the degree symbol when gridding your answer.)","stimulus":"The figure presents two triangles, triangle A, B C and triangle D E F. The two triangles are placed side by side, and triangle A, B C is larger than triangle D E F. In triangle A, B C, side A, B slants upward and to the right, side B C slants downward and to the right, and side A, C slants slightly upward and to the right. In triangle D E F, side D E slants upward and to the right, side E F slants downward and to the right, and side D F slants slightly upward and to the right. A note indicates that the figures are not drawn to scale.","stimulus_html":"<div class=\"stimulus_reference \">\n        <div class=\"standalone_image \">\n          <img src=\"/api/assets/fa6ee0bbe6e118a506170e5eef6d30c21e81cc9b3a32acac4ac7467c36882d8f\" alt=\"The figure presents two triangles, triangle A, B C and triangle D E F. The two triangles are placed side by side, and triangle A, B C is larger than triangle D E F. In triangle A, B C, side A, B slants upward and to the right, side B C slants downward and to the right, and side A, C slants slightly upward and to the right. In triangle D E F, side D E slants upward and to the right, side E F slants downward and to the right, and side D F slants slightly upward and to the right. A note indicates that the figures are not drawn to scale.\" width=\"210\" height=\"83\"></div>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">Triangle <span class=\"italic\">ABC</span> and triangle <span class=\"italic\">DEF</span> are shown. The relationship between the side lengths of the two triangles is such that <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1bfc62ca9d6ee5f02a4daf35321d31bb4be0a82e7787a01a365678a92ceca1a6\" alt=\"the length of side A, B, over, the length of side D E, equals, the length of side B C, over, the length of side E F, which equals, the length of side A, C, over, the length of side D F, which equals 3\"></span></span>. If the measure of angle <span class=\"italic\">BAC</span> is 20°, what is the measure, in degrees, of angle <span class=\"italic\">EDF</span> ? (Disregard the degree symbol when gridding your answer.)</p>\n","rationale_html":"<p>The correct answer is 20. By the equality given, the three pairs of corresponding sides of the two triangles are in the same proportion. By the side-side-side (SSS) similarity theorem, triangle<span class=\"italic\"> ABC</span> is similar to triangle <span class=\"italic\">DEF</span>. In similar triangles, the measures of corresponding angles are congruent. Since angle <span class=\"italic\">BAC</span> corresponds to angle <span class=\"italic\">EDF</span>, these two angles are congruent and their measures are equal. It’s given that the measure of angle<span class=\"italic\"> BAC </span>is 20°, so the measure of angle <span class=\"italic\">ED</span><span class=\"italic\">F</span> is also 20°.</p>\n","correct_answer":["20"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.621000+00:00","source_updated_at":"2023-08-02T20:25:59.621000+00:00","options":[],"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}}