Question

如图,在Rt△ABC中,∠ACB=90°,D,E在AC上,且AB=AD,CB=CE.

Answer 1

用等腰三角形顶角与底角的数量关系,加上三角形内角和可得.

∵AB=AD,∴∠ADB=1/2(180°-∠A)

∵CB=CE,∴∠CEB=1/2(180°-∠C),

∴∠EBD=180°-(∠ADB+∠CEB)

=180°-［180°-1/2(∠A+∠C)］

=1/2(∠A+∠C)

=90°-1/2∠B.

①当∠ABC=45°时,∠EBD=45°,

②当∠ABC=100°时,∠EBD=40°,

③当∠ABC=α时,∠EBDE=90°-1/2α.