1988 AMC 8 第 9 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
9.
等腰三角形是有两条边长度相等的三角形。下面方格图中的五个三角形中，有多少个是等腰三角形？
An isosceles triangle is a triangle with two sides of equal length. How many of the five triangles on the square grid below are isosceles?
小提示：
从方格中找每个三角形的边长：一条斜边横跨 格、竖跨 格，则长度为 。有两边相等时就是等腰三角形。
Find each triangle’s side lengths from the grid: a slanted side spanning across and up has length A triangle is isosceles when two of its sides are equal.
大提示：
算出五个三角形各自的三条边长，寻找相等的一对；只有一个三角形三边都不同。
Work out all three side lengths for each of the five triangles and look for a matching pair; only one triangle ends up with three different side lengths.
解答：
从方格中读出每个三角形的边长。水平或竖直边可直接数格子；一条斜边横跨 个单位、竖跨 个单位，长度为 。
左上三角形：两条斜边都横跨 、竖跨 ，所以长度都为 ，底边长 。有两边相等，所以是等腰三角形。
上方中间三角形：它有一条长 的竖边和一条长 的横边（第三边是斜边 ）。有两边相等，所以是等腰三角形。
右上三角形：边长是 、 和 ，三者都不同，所以不是等腰三角形。
左下（宽而扁的）三角形：两条斜边都横跨 、竖跨 ，所以长度都为 。有两边相等，所以是等腰三角形。
右下三角形：其中两条边都横跨 和 （长度为 ），第三边为 。有两边相等，所以是等腰三角形。
五个三角形中有四个是等腰三角形。
所以正确答案是 D。
Read each triangle’s side lengths from the grid. A horizontal or vertical side is counted directly, and a slanted side spanning units across and units up has length
Top-left triangle: its two slanted sides each span across and up, so each has length with a base of length Two equal sides, so it is isosceles.
Top-middle triangle: it has a vertical side of length and a horizontal side of length (its third side is the slant ). Two equal sides, so it is isosceles.
Top-right triangle: its sides are and which are all different, so it is not isosceles.
Bottom-left (wide, flat) triangle: its two slanted sides each span across and up, so each has length Two equal sides, so it is isosceles.
Bottom-right triangle: two of its sides each span and (giving length ), while the third is Two equal sides, so it is isosceles.
Four of the five triangles are isosceles.
Thus, the correct answer is D .
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