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在几何问题中,中点问题是一类常见的问题.与中点有关的辅助线有以下几种.一、已知三角形两边中点,连结两个中点构造三角形的中位线例1 如图1,□ABCD的对角线BD、AC相交于点O,DB=AB,E是AB的中点,DE交AC于点F.求证:(1)∠BDE=∠DCA;(2)FD=FA.(温州97年中考题)分析 因为ABCD平行四边形,故O是BD中点,又E是AB的中点,连结OE,则OE是△ABD的中位线,可证ADOE是等腰梯形.证明 连结OE.
In the geometric problem, the midpoint problem is a common problem. The auxiliary lines related to the midpoint are as follows. 1. The midpoints of the two sides of the triangle are known, and the midline of the triangles connecting two midpoints is constructed. Example 1 In Fig. 1, the diagonal lines BD and AC of □ABCD intersect at the point O, DB=AB, E is the midpoint of AB, and DE is AC at point F. Proof: (1) ∠BDE=∠DCA; (2)FD = FA. (Wenzhou 97 exam questions) Analysis Because ABCD parallelogram, so O is the BD midpoint, and E is the midpoint of AB, link OE, OE is the median line of △ ABD, can prove that ADOE is isosceles Trapezoidal. Attestation link OE.