Question

如图,在△ABC中,点E在BC上,点D在AE上,已知∠ABD=∠ACD,∠BDE=∠CDE.求证BE=CE.

Answer 1

因为∠BDE=∠CDE,∠BDA=∠CDA,且AD=AD,∠ABD=∠ACD,所以△ADE全等于△ADC.

所以AB=AC,∠BAE=∠CAE,且AE=AE,所以△ABE全等于△ACE,所以BE=CE.