如图,在菱形abcd中,ab=bd,点e·f分别在ab·cd上,且ae=df,bf与de相交于点g.求DG+BG=CG

问题描述:

如图,在菱形abcd中,ab=bd,点e·f分别在ab·cd上,且ae=df,bf与de相交于点g.求DG+BG=CG

证明:延长GB至M使BM=DG,连接CM∵四边形ABCD为菱形∴AB=BC=CD=AD ∵AB=BD∴AB=BC=CD=AD=BD∴△ABD,△BCD为等边三角形∴∠ADB=∠CDB=∠CBD=∠A=60°∵AE=DF ∴△ADE≌△DBF∴∠1=∠2∴∠CDG=∠ADB+∠CDB-∠2=...