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1.概念不清例1 若空间四边形ABCD中,E、G、F分别为AD、DB、BC的中点,∠EGF是异面直线AB与CD所成的角吗?为什么?错解因为E、G、F分别为图1AD、DB、BC的中点,所以EG∥AB,GF∥DC,故∠EGF是AB与CD所成的角.剖析对异面直线所成角的概念只注意了平行条件而忽略了角的允许值范围,根据定义直线EG和FG所夹的锐角(或直角)才是AB与CD所成的角,而题中没有给出∠EGF的范围,故不能确定该角是否为AB与CD所成的角.
1. Unclear Concept 1 If the space quadrangle ABCD, E, G, and F are the midpoints of AD, DB, and BC, respectively, is ∠EGF the angle formed by the straight lines AB and CD? Why? G, F are the midpoints of Figure 1 AD, DB, and BC, respectively, so EG ∥ AB, GF ∥ DC, so ∠ EGF is the angle formed by AB and CD. Analysis of the concept of the angle formed by a straight line on the opposite side only pay attention to The parallel condition ignores the allowable value range of the angle. According to the definition, the acute angle (or right angle) between the straight lines EG and FG is the angle formed by AB and CD. However, the range of ∠EGF is not given in the question, so it cannot be determined. Is the angle between AB and CD?