∠BGD=∠BAG+∠ABG=1/2(∠BAC+∠ABC)
∠CGH=90°-∠GCH=90°-1/2∠ACB
∵∠BAC+∠ABC+∠ACB=180°
∴∠BAC+∠ABC=180°-∠ACB
∴1/2(∠BAC+∠ABC)=90°-1/2∠ACB
即∠BGD=∠CGH
∠BGD=∠BAG+∠ABG=1/2(∠BAC+∠ABC)
∠CGH=90°-∠GCH=90°-1/2∠ACB
∵∠BAC+∠ABC+∠ACB=180°
∴∠BAC+∠ABC=180°-∠ACB
∴1/2(∠BAC+∠ABC)=90°-1/2∠ACB
即∠BGD=∠CGH