Question

（本小題滿分7分）如圖，四邊形中，，
平分，交于．

【小題1】（1）求證：四邊形是菱形；
【小題2】（2）若點是的中點，試判斷的形狀，并說明理由．

Answer 1

【小題1】（1），即，又，四邊形是平行四邊形．
····································································································· （2分）
平分，，················································ （3分）
又，，，，
四邊形是菱形．
【小題2】（2）證法一：是中點，．
又，，，······································· （5分）
，··························································· （6分）
，．
即，是直角三角形．··············································· （7分）
證法二：連，則，且平分，·········································· （5分）
設交于．
是的中點，．························································· （6分）
，是直角三角形．解析:
略