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SAT官方每日一题：2011年9月25日

2012-03-04来源:互联网

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　　2011年9月25日

　　考试类型:Mathematics > Standard Multiple Choice

　　Read the following SAT test question and then click on a button to select your answer.

　　Which of the following statements must be true of the lengths of the segments on line above?

　　 Roman number 1 . A B + C D = A D

　　 Roman numeral 2 . A B + B C = A D minus C D

　　 Roman numeral 3 . A C minus A B = A D minus C D

　　A. Roman numeral 1 only

　　B. Roman numeral 2 only

　　C. Roman numeral 3 only

　　D. Roman numeral 1 and Roman numeral 2 only

　　E. Roman numeral 1 , Roman numeral 2 , and Roman numeral 3

正确答案:B

解析:

Consider each statement separately. For example, consider statement Roman numeral 1 , A B + C D equals A D . From the figure, you can see that segment A D is made up of the segments A B , B C , and C D . This tells you that cannot equal A D , since B C cannot equal zero. Statement is not true.

Consider statement Roman numeral 2 , A B + B C equals A D minus C D . Since is between and , it follows that A B + B C equals A C . Since is between and , it follows that A C + C D equals A D . Therefore, A D minus C D = A C . Since both and equal A C , they are equal to each other. Statement is true.

Consider statement Roman numeral 3 , A C minus A B equals A D minus C D . The left side of the equation, , is equivalent to B C . The right side of the equation, , is equivalent to A C . Since A B cannot equal zero, B C is not equal to A C . Statement is not true.