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SAT数学题练习两道

　　下面是两道数学题，都是关于几何方面的，大家可以在备考SAT数学考试的时候对此进行适当的练习。SAT数学题对于中国考生的作用，大部分都是用来熟悉题型和解答方法，而不是作为知识点的积累，所以大家在备考的时候，一定要抓住重点。

　　

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　　If triangle A B Cabove is congruent to triangle D E F(not shown), which of the following must be the length of one side of triangle D E F?

 

　　Answer Choices

　　(A) 18

 

　　(B) 24

 

　　(C) 3 times (square root 6)

 

　　(D) 6 times (square root 3)

 

　　(E) It cannot be determined from the information given.

　　The correct answer is D

　　Explanation

　　Triangle A B Cis congruent to triangle D E F, so the lengths of the three sides of triangle D E Fare the same as the lengths of the three sides of triangle A B C. Triangle A B Cis a 30 degrees- 60 degree- 90 degreestriangle with hypotenuse of length 12, so the other two sides of triangle A B Chave lengths 6and 6 times (square root 3). Therefore, the lengths of the sides of triangle D E Fmust be 12, 6, and 6 times (square root 3). Of the choices given, only 6 times (square root 3)is one of these values.

　　

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　　If two sides of the triangle above have lengths 5and 6, the perimeter of the triangle could be which of the following?

 

　　Roman numeral 1. 11　　Roman numeral 2. 15　　Roman numeral 3. 24

 

　　Answer Choices

　　(A) Roman numeral 1only

 

　　(B) Roman numeral 2only

 

　　(C) Roman numeral 3only

 

　　(D) Roman numeral 2and Roman numeral 3only

 

　　(E) Roman numeral 1, Roman numeral 2, and Roman numeral 3

 

　　The correct answer is B

　　Explanation

　　Difficulty: Hard

　　In questions of this type, statements Roman numeral 1, Roman numeral 2, and Roman numeral 3should each be considered independently of the others. You must determine which of those statements could be true.

 

　　Statement Roman numeral 1cannot be true. The perimeter of the triangle cannot be 11, since the sum of the two given sides is 11without even considering the third side of the triangle.

 

　　Continuing to work the problem, you see that in Roman numeral 2, if the perimeter were 15, then the third side of the triangle would be 15 minus (6 + 5), or 4. A triangle can have side lengths of 4, 5, and 6. So the perimeter of the triangle could be 15.

 

　　Finally, consider whether it is possible for the triangle to have a perimeter of 24. In this case, the third side of the triangle would be 24 minus (6 + 5) = 13. The third side of this triangle cannot be 13, since the sum of the other two sides is not greater than 13. By the Triangle Inequality, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So the correct answer is Roman numeral 2only.

　　以上就是这两道SAT数学题的全部内容，都是选择题型，来自SAT考试官方网站，后面附有详细的答案解析。大家可以在备考SAT数学考试的时候，根据自己的思考过程了解一些SAT数学考试中几何方面的知识。

更多SAT数学相关：

SAT数学练习题一道

6道SAT数学练习题

SAT数学练习题六道(代数)

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