Question

如图,在△ABC中,AD⊥BC于D,AD与BE相交于H,且BH=AC,DH=DC,那么∠ABC=?°

Answer 1

∵AD⊥BC,∴∠BDH=∠ADC=90°,

∵BH=AC,DH=DC,

∴RTΔBDH≌RTΔADC(HL),

∴BD=AD,

∴ΔABD是等腰直角三角形,

∴∠ABC=45°.