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題目列表(包括答案和解析)

已知△ABC,AC=BC,CD⊥AB于點(diǎn)D,點(diǎn)F在BD上,連接CF,AM⊥CF于點(diǎn)M,AM交CD于點(diǎn)E.
(1)如圖1,當(dāng)∠ACB=90°時(shí),求證:DE=DF;
(2)如圖2,當(dāng)∠ACB=60°時(shí),DE與DF的數(shù)量關(guān)系是______
(3)在2的條件若tan∠EAF=數(shù)學(xué)公式,EM=數(shù)學(xué)公式,連接EF,將∠DEF繞點(diǎn)E逆時(shí)針旋轉(zhuǎn),旋轉(zhuǎn)后角的兩邊交線段CF于N、G兩點(diǎn),交線段BC于P、T兩點(diǎn)(如圖3),若CN=3FN,求線段GT的長(zhǎng).

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(2011•香坊區(qū)模擬)已知△ABC,AC=BC,CD⊥AB于點(diǎn)D,點(diǎn)F在BD上,連接CF,AM⊥CF于點(diǎn)M,AM交CD于點(diǎn)E.
(1)如圖1,當(dāng)∠ACB=90°時(shí),求證:DE=DF;
(2)如圖2,當(dāng)∠ACB=60°時(shí),DE與DF的數(shù)量關(guān)系是
DF=
3
DE
DF=
3
DE

(3)在2的條件若tan∠EAF=
3
4
,EM=
9
19
19
,連接EF,將∠DEF繞點(diǎn)E逆時(shí)針旋轉(zhuǎn),旋轉(zhuǎn)后角的兩邊交線段CF于N、G兩點(diǎn),交線段BC于P、T兩點(diǎn)(如圖3),若CN=3FN,求線段GT的長(zhǎng).

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