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As shown in the figure, there are two intersecting line segments Mn, EF in square ABCD, m, N, e, f on edge AB, CD, ad, BC respectively. Student a thinks: if Mn = EF, then Mn ⊥ EF; student B thinks: if Mn ⊥ EF, then Mn = ef. Do you think () A. Neither is right. B. both are right. C. only a is right. D. only B is right
Let EF and Mn intersect at point O, MP and EF intersect at point Q, ∵ quadrilateral ABCD is a square, ∵ eg = MP, for example, in RT △ EFG and RT △ MNP, Mn = efeg = MP, ≌ RT △ EFG ≌ RT △ MNP (HL), ∵ MNP = ∵ EFG, ≌ MP ⊥ CD, ∵ C = 90 °, ∵ MP ∥ BC, ≌ EQM = ≌ EFG = ≌ MNP, and ∵ m In △ MOQ, ∠ MOQ = 180 ° - (∠ EQM + ∠ NMP) = 180 ° - 90 ° = 90 ° and 〈 Mn ⊥ EF, when e moves to D and f moves to B, Mn = EF is not vertical, so a is not correct. For student B's words: ∵ mp ⊥ CD, ∵ C = 90 °, ∵ MP ∥ BC, ∥ EQM = ∥ EFG, ∥ Mn ⊥ EF, ∥ NMP + ∠ EQM = 90 ° and ∥ MP ⊥ CD, ∥ nm In △ EFG and △ MNP, ∠ EFG = MNP, in △ EFG and △ MNP, ∠ EFG = MNP, EGF = MPN = 90 ° eg = MP, AAS, AAS, AAS, AAS and EF, respectively, so the statement of student B is correct. To sum up, only the statement of student B is correct
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