Question

如图,△ABC中,AB=AC,∠ADB＞∠ADC,求证DC＞DB

Answer 1

将△ABD逆时针旋转,使得AB与AC重合,得△ACE,则有AD=AE,CE=BD,∠AEC=∠ADB连结DE,在△ADE中,AD=AE,所以∠ADE=∠AED,因为∠ADB＞∠ADC,所以∠ADC＜∠AEC,所以∠CDE＜∠CED,根据大角对大边定理可知：CE＞CD,即BD＞CD