Question

21 已知：如图,在□ABCD中,BE=DF,AG=CH,求证：四边形GEHF是平行四边形.

Answer 1

⑴证明：△AEG≌△CFH﹙SAS﹚：∵四边形ABCD是平行四边形,∴AB∥=DC,而BE=DF,∴AE=CF,∠EAG=∠FCH,AG=CH,∴△AEG≌△CFH,∴EG=FH.⑵证明：△AEH≌△CFG：AE=CF,∠EAH=∠FCG,AH=AG＋GH=CH＋GH=CG,∴△EAH≌△FCG﹙SAS﹚,∴EH=FG,∴四边形GEHF是平行四边形﹙两组对边分别相等的四边形是平行四边形﹚.