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三垂线定理 习题课

P. a. o. A. α. 三垂线定理 习题课. 练习： 已知：∠ BAC 在平面 α 内， PO α ， PO⊥ 平面 α 于 O ．如果 ∠ PAB ＝∠ PAC ． 求证：∠ BAO ＝∠ CAO ．. 例 1  如图 2 ，已知： PA⊥PB ， PA⊥PC ， PB⊥PC ． PH⊥ 平面 ABC 于 H ．求证： (1)H 点是△ ABC 的垂心． (2) △ABC 是锐 角三角形。. 例 2 如图，△ ABC 中，∠ BAC 是锐角， PA⊥ 平面 ABC 于 A ， AO⊥ 平面 PBC 于

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三垂线定理 习题课

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  1. P a o A α 三垂线定理 习题课

  2. 练习：已知：∠BAC在平面α内， POα，PO⊥平面α于O．如果 ∠PAB＝∠PAC． 求证：∠BAO＝∠CAO．

  3. 例1  如图2，已知：PA⊥PB，PA⊥PC， PB⊥PC．PH⊥平面ABC于H．求证： (1)H点是△ABC的垂心．(2) △ABC是锐 角三角形。

  4. 例2 如图，△ABC中，∠BAC是锐角， PA⊥平面ABC于A，AO⊥平面PBC于 O．求证：O不可能是△PBC的垂心．

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