{"id":"cb_question_bank:d960ac42-d74d-4b4f-9c73-411254f6ae3f","source_id":"cb_question_bank","source_item_id":"d960ac42-d74d-4b4f-9c73-411254f6ae3f","external_id":null,"ibn":"05758-DC","question_id":"dba6a25a","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.C.","skill":"Right triangles and trigonometry","difficulty":"H","score_band":6,"answer_type":"spr","answer_source":"rationale","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"In the figure above, line segment B D is parallel to line segment A, E . What is the length of line segment C E ?","stimulus":"The figure presents triangle A, C E, with horizontal side A, C. Side A, E, is perpendicular to side A, C, such that point E, is above point A. Point B, lies on horizontal side A, C, point D, lies on hypotenuse C E, and line segment B D, is drawn such that it is parallel to side A, E, and forms triangle C D B. Side A, E, is labeled 18, side B C, is labeled 8, side B D, is labeled 6, and a right angle symbol is at point A","stimulus_html":"
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In the figure above, \"line is parallel to \"line. What is the length of \"line ?

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The correct answer is 30. In the figure given, since \"side is parallel to \"side and both segments are intersected by \"side, then angle BDC and angle AEC are corresponding angles and therefore congruent. Angle BCD and angle ACE are also congruent because they are the same angle. Triangle BCD and triangle ACE are similar because if two angles of one triangle are congruent to two angles of another triangle, the triangles are similar. Since triangle BCD and triangle ACE are similar, their corresponding sides are proportional. So in triangle BCD and triangle ACE, \"side corresponds to \"side and \"side corresponds to \"side. Therefore, \"the. Since triangle BCD is a right triangle, the Pythagorean theorem can be used to give the value of CD: \"6. Taking the square root of each side gives \"the. Substituting the values in the proportion \"the yields \"6. Multiplying each side by CE, and then multiplying by \"10 yields \"the. Therefore, the length of \"side is 30.

\n","correct_answer":["30"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.630000+00:00","source_updated_at":"2023-08-02T20:25:59.630000+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}}