Question

．（本小題滿分7分）已知：正方形中，，繞點(diǎn)順時(shí)針旋轉(zhuǎn)，它的兩邊分別交（或它們的延長(zhǎng)線）于點(diǎn)．當(dāng)繞點(diǎn)旋轉(zhuǎn)到時(shí)（如圖1），易證．

1.（1）當(dāng)繞點(diǎn)旋轉(zhuǎn)到時(shí)（如圖2），線段和之間有怎樣的數(shù)量關(guān)系？寫出猜想，并加以證明．

2.（2）當(dāng)繞點(diǎn)旋轉(zhuǎn)到如圖3的位置時(shí)，線段和之間又有怎樣的數(shù)量關(guān)系？請(qǐng)直接寫出你的猜想．

 

 

 

Answer 1

 

1.解：（1）成立．······································································ （2分）

如圖，把繞點(diǎn)順時(shí)針，得到，

則可證得三點(diǎn)共線（圖形畫正確）······ （3分）

證明過程中，

證得：·································· （4分）

證得：····························· （5分）

······························································································· （6分）

 

2.（2）  （8分）

 

解析:略