Question

如图3是由图1的△ABC沿DE折叠得到的,猜想∠BDA+∠CEA与∠A的关系,并说明理由

Answer 1

如图

∠ADE=∠A'DE,∠AED=∠A'ED

所以,∠BDA+∠CEA=(180°-∠A'DA)+(180°-∠A'EA)

=180°-2∠A'DE+180°-2∠A'ED

=360°-2(∠A'DE+∠A'ED)

=360°-2(180°-A')

=2A'

=2A