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现行初级中学课本平面几何关于中心对称的定理的证明为: 定理如果作一条线段的两个端点关于一个已知点的对称点,那末: (1)连结这两个点的线段平行于已知线段,并且和已知线段相等。 (2)已知线段上任何一点的对称点,都在所作的线段上。求证(2) AB上任何一点的对称点都在所作的线段上。证明(2) 在AB上任取一点M,连结MO,并且延长MO交B′A′于M′。在ΔA′OM′和ΔAOM中∠2=∠1(平行线的内错角相等)。∠4=∠3(对顶角相等)OA′=OA;
The proof of the theorem of plane symmetry about central symmetry in current junior middle school textbooks is: Theorem If you make the symmetry points of two ends of a line segment about a known point, then: (1) The line segment connecting the two points is parallel to the known line segment. , and is equal to the known line segment. (2) The point of symmetry at any point on the known line segment is on the line segment. Proof (2) The point of symmetry at any point on AB is on the line segment. Proof (2) Take any point M on AB, link MO, and extend MO to B’A’ to M’. In ΔA′OM′ and ΔAOM, ∠2=∠1 (the parallel misalignment angle is equal). ∠ 4 = ∠ 3 (equal to the top angle) OA’ = OA;