2. 外语
  3. Is △ABC isosceles? (1)∠A and∠B don’t have the same measure. (2)∠A and∠B have the same measure.

Is △ABC isosceles? (1)∠A and∠B don’t have the same measure. (2)∠A and∠B have the same measure.

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问题 Is △ABC isosceles?
(1)∠A and∠B don’t have the same measure.
(2)∠A and∠B have the same measure.
选项 A、Statement (1) ALONE is sufficient, but statement (13) alone is not sufficient to answer the question asked.
B、Statement (2) ALONE is sufficient, but statement (12) alone is not sufficient to answer the question asked.
C、BOTH statement (1) and (13) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
D、EACH statement ALONE is sufficient to answer the question asked.
E、Statement (1) and(13)TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
答案B
解析 三角形中如果两个角相等，它们各自所对应的边当然也相等，此三角形必然为等腰三角形。单独(1)：∠A和∠B不相等，无法判定它们是否等于AC，那么也无法判定它们是否为等腰三角形；单独(2)：已经告诉我们有两个角相等，那么这个三角形当然是等腰三角形。所以B为正确答案。
直角三角形(right triangle)：有一个角为直角的三角形。
直角三角形中最长的边为斜边(hypotenuse)，其他两边称为腰(legs)；直角三角形满足勾股定理(pythagorean theorem)，即a2+b2=c2；如果三角形三条边的比是3：4：5，那么这个三角形是直角三角形。
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