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  3. For each of Questions 1 to 9, compare Quantity A and Quantity B, using additional information centered above the two quantities

For each of Questions 1 to 9, compare Quantity A and Quantity B, using additional information centered above the two quantities

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问题 For each of Questions 1 to 9, compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given. Select one of the following four answer choices and fill in the corresponding oval to the right of the question.
(A)Quantity A is greater.
(B)Quantity B is greater.
(C)The two quantities are equal.
(D)The relationship cannot be determined from the information given.
A symbol that appears more than once in a question has the same meaning throughout the question.

选项
答案A
解析 One way you can solve this problem is by using the following fact:
    If ABC is a triangle and the measure of angle A is greater than the measure of angle B, then the side opposite angle A is longer than the side opposite angle B.
    Since the third angle of the triangle measures 40°, you can use the fact above to conclude that the side opposite the 50° angle is longer than the side opposite the 40° angle. So x >y, and x/y> 1, which yields Choice A.
    You can also solve this problem without using the fact above. Instead, you can use the strategy of adapting solutions to related problems to determine the relationship between x and y.
    Note that the angles in the triangle differ only a little from the angles in a 45° - 45° - 90° triangle. How do the lengths of the legs of a 45° - 45° - 90° triangle compare to the lengths of the legs of the triangle in the question? To make the comparison, add a line segment to the triangle so that the line segment cuts the 50° angle in two parts, making a 45° angle with the horizontal base, as shown in the following figure:

    The 45° - 45° - 90° triangle has two 45° angles, so z = y, and z/y = 1. Since z/y = 1 and x > z, it follows that x/y > 1. The correct answer is Choice A.
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