{"id":221830,"date":"2024-08-09T08:41:22","date_gmt":"2024-08-09T13:41:22","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=221830"},"modified":"2025-07-31T17:47:50","modified_gmt":"2025-07-31T22:47:50","slug":"email-9-tsi-qod-answer","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/email-9-tsi-qod-answer\/","title":{"rendered":"TSI Question of the Day"},"content":{"rendered":"
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<\/span>Answer<\/h2>\n
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  1. 5 units<\/span><\/li>\n<\/ol>\n
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    The two right triangles are similar because they share a pair of vertical angles (\u2220ACB and \u2220ECD). Vertical angles are always congruent. Obviously both right angles (\u2220B and \u2220D) are congruent. Thus, angles A and E are congruent because of the triangular sum theorem.<\/p>\n

    With similar triangles, corresponding sides will be proportional. Segment \\(\\overline{\\mathit{BC}}\\) is half the length of \\(\\overline{\\mathit{CD}}\\), therefore \\(\\overline{\\mathit{AC}}\\) will be half the length of \\(\\overline{\\mathit{CE}}\\). The length of \\(\\overline{\\mathit{CE}}\\) can be computed from the Pythagorean theorem, since it is the hypotenuse of a right triangle for which the lengths of the other two sides are known:<\/p>\n

    \\(\\overline{\\mathit{CE}} = \\sqrt{6^{2} + 8^{2}} = \\sqrt{100} = 10\\)<\/p>\n

    The length of \\(\\overline{\\mathit{AC}}\\) will be half of this value, or 5 units.<\/p>\n<\/div>\n<\/div>\n

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    \n Review the question<\/span>
    \n \uff0b<\/span>\n <\/div>\n
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    \"A<\/p>\n

    In the figure above, segment BC is 4 units long, segment CD is 8 units long, and segment DE is 6 units long. What is the length of segment AC?<\/p>\n

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    1. 4 units<\/li>\n
    2. 5 units<\/li>\n
    3. 6 units<\/li>\n
    4. 8 units<\/li>\n<\/ol><\/div>\n<\/p><\/div>\n<\/div>\n<\/div>\n

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