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证明等比式(或等积式)方法较多,利用“相似三角形的对应边成比例”证明等比式是应用广泛的一种证法。我们可以引导学生将一系列此类命题进行合理“转化”,再回到这种证法上来。1.问:如何利用相似三角形证明等比式?答:只须观察所证等比式每端所含的三个字母所表示的点能否构成三角形。若能构成三角形,证明其相似即可。例1 在ΔABC中,D为BC上一点,且∠BAC=∠ADC(图1)求证:(AB)/(BC)=(AD)/(AC).
Prove that there are many equal-ratio (or iso-integration) methods, and use the “proportional to the corresponding sides of a similar triangle” to prove that the equal ratio is a widely used proof. We can guide students to make a reasonable “transformation” of a series of such propositions and return to this proof. 1.Q: How to use equal triangles to prove the analogy? A: Just observe whether the points represented by the three letters at each end of the test pattern can form triangles. If you can form a triangle, prove it is similar. Example 1 In ΔABC, D is a point on BC, and ∠BAC=∠ADC (Figure 1) verification: (AB)/(BC)=(AD)/(AC).