世界上最难的简单几何题
你只能使用初等几何原理来解这道题，也就是说只能使用三角形的内角总和是180度；等腰和等边三角形的特性；平行线的对顶角相等；全等三角形的角边角、边角边、边边边定理以及三角形相似的角角角定理这一类的基础知识。不能使用正弦余弦定理。关于能使用的定理会在下文给出。
这是我所见过的最难的数学题，尽管看起来是如此的简单。并且真的可以只用初等几何解题。
Using only elementary geometry, determine angle x. Provide a step-by-step proof.
You may only use elementary geometry, such as the fact that the angles of a triangle add up to 180 degrees and the basic congruent triangle rules (side-angle-side, etc.). You may not use more advanced trigonomery, such as the law of sines, the law of cosines, etc. There is a review of elementary geometry below.
This is the hardest problem I have ever seen that is, in a sense, easy. It really can be done using only elementary geometry. This is not a trick question.
这里有一个小提示。
Triangle Problem 1 Scale Diagram
Your working diagram should be large and accurate. Draw the diagram yourself using a protractor or print this correctly scaled diagram.
这里还有另一个小提示。
Triangle Problem 1 Small Hint
To solve the problem, you will need to draw a few more lines inside the triangle.
You will need to do more than merely adding and subtracting angles.
The solution has more steps than you might expect.
这道题排行第二
World's Second-Hardest Easy Geometry Problem
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仅能使用初等几何原理得出角X的值。并写出详细步骤。 这道题是上一题的变形，但是要解出来也绝非易事。 Using only elementary geometry, determine angle x. Provide a step-by-step proof. This is a variation of the problem above. This is also a very hard problem that is, in a sense, easy.
这里有一个小提示。 |
Triangle Problem 2 Scale Diagram
Your working diagram should be large and accurate. Draw the diagram yourself using a protractor or print this correctly scaled diagram.
这里还有另一个小提示。
Triangle Problem 2 Small Hint
To solve the problem, you will need to draw a few more lines inside the triangle.
You will need to do more than merely adding and subtracting angles.
The solution has more steps than you might expect.
Problem 2 is not solved in the same way as problem 1.
基础几何原理
关于解题你所能用的原理。
相交线和交角：两条相交线，对角相等，两个邻角相加为180度。两条平行线与第三条线相交，相对的角相等。
三角形：三角形的内角总和是180度。等腰三角形有两条边相等，且有两个相等角。等边三角形三条边相等，三个角相等。直角三角形有一个九十度的角。两个三角形的形状相似，则它们的对应角相等。
- 边角边：有两边和它的夹角对应相等的两个三角形全等
- 边边边：三边对应相等的两个三角形全等
- 角边角：两个角和两角夹的边对应相等的三角形全等
- 角角：如果两个三角形的两个对应角相等，那么这两个三角形相似
