如图，已知线段AB的同侧有两点C、D满足∠ACB=∠ADB=60°，∠ABD=90°-12∠DBC．求证：AC=AD．

Question

如图，已知线段AB的同侧有两点C、D满足∠ACB=∠ADB=60°，∠ABD=90°-(1)/(2)∠DBC．求证：AC=AD．

Answer 1

证明：以AB为轴作△ABC的对称△ABC′，如图：则AC=AC′，∠C=∠C′=60°，∠ABC′=∠ABC，因为∠ABD=90°-12∠DBC所以2∠ABD+∠DBC=180°所以∠ABD+∠DBC+∠ABD=180°即∠ABC+∠ABD=180°所以∠ABC′+∠ABD=180°所...