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26. (1)如圖1.圖2.圖3.在中.分別以為邊.向外作正三角形.正四邊形.正五邊形.相交于點(diǎn). ①如圖1.求證:, ②探究:如圖1. , 如圖2. , 如圖3. . (2)如圖4.已知:是以為邊向外所作正邊形的一組鄰邊,是以為邊向外所作正邊形的一組鄰邊.的延長相交于點(diǎn). ①猜想:如圖4. (用含的式子表示), ②根據(jù)圖4證明你的猜想. (1)①證法一:與均為等邊三角形. .························································································ 2分 且··············································· 3分 . 即························································ 4分 .··················································· 5分 證法二:與均為等邊三角形. .························································································ 2分 且························································································ 3分 可由繞著點(diǎn)按順時針方向旋轉(zhuǎn)得到··································· 4分 .··························································································· 5分 ②...········································································ 8分 (2)①········································································································ 10分 ②證法一:依題意.知和都是正邊形的內(nèi)角... .即.····························· 11分 .·························································································· 12分 ..······ 13分 . ········································ 14分 證法二:同上可證 .··························································· 12分 .如圖.延長交于. . ································ 13分 ················· 14分 證法三:同上可證 .··························································· 12分 . . ························································ 13分 即········································································ 14分 證法四:同上可證 .··························································· 12分 .如圖.連接. .···································· 13分 即······························· 14分 注意:此題還有其它證法.可相應(yīng)評分. 查看更多

 

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從2010年3月23日福建南平發(fā)生校園慘案以來,全國某些地方相繼發(fā)生類似的校園慘案,為了“打造平安校園,優(yōu)化育人環(huán)境”,重慶市交巡警總隊決定在小龍坎正街上設(shè)立一個交巡警平臺P點(diǎn),要求巡警從該平臺到南開中學(xué)和第八中學(xué)這兩所中學(xué)的總距離之和最短.請你用尺規(guī)作圖的方式找出交巡警平臺P點(diǎn)的位置.(不寫出已知、求作、作法,不用說明理由,但要保留作圖痕跡)

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如圖,正比例函數(shù)與反比例函數(shù)相交于A、B點(diǎn),已知點(diǎn)A的坐標(biāo)為(4,n),BD⊥x軸于點(diǎn)D,且S△BDO=4。過點(diǎn)A的一次函數(shù)與反比例函數(shù)的圖像交于另一點(diǎn)C,與x軸交于點(diǎn)E(5,0)。

(1)求正比例函數(shù)、反比例函數(shù)和一次函數(shù)的解析式;

(2)結(jié)合圖像,求出當(dāng)時x的取值范圍。

         第26題

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已知拋物線My = -x2+2mx+nm,n為常數(shù),且m> 0,n>0)的頂點(diǎn)為A,與y軸交于點(diǎn)C;拋物線N與拋物線M關(guān)于y軸對稱,其頂點(diǎn)為B,連結(jié)AC,BCAB

問拋物線M上是否存在點(diǎn)P,使得四邊形ABCP為菱形?如果存在,請求出m的值;如果不存在,請說明理由.

說明:⑴如果你反復(fù)探索,沒有解決問題, 請寫出探索過程(要求至少寫3步);

⑵在你完成⑴之后,可以從①、②中選取一個條件,完成解答(選取①得7分;選、诘10分).

;②

附加題: 若將26題中“拋物線My= -x2+2mx+nm,n為常數(shù),且m> 0,n>0) ”改為“拋物線My= ax2+2mx+nm,n為常數(shù),且m≠ 0,a≠0, n>0) ”,其他條件不變, 探究 26題中問題.

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已知拋物線My = -x2+2mx+nm,n為常數(shù),且m> 0,n>0)的頂點(diǎn)為A,與y軸交于點(diǎn)C;拋物線N與拋物線M關(guān)于y軸對稱,其頂點(diǎn)為B,連結(jié)AC,BCAB

問拋物線M上是否存在點(diǎn)P,使得四邊形ABCP為菱形?如果存在,請求出m的值;如果不存在,請說明理由.

說明:⑴如果你反復(fù)探索,沒有解決問題, 請寫出探索過程(要求至少寫3步);

⑵在你完成⑴之后,可以從①、②中選取一個條件,完成解答(選、俚7分;選、诘10分).

;②

附加題: 若將26題中“拋物線My= -x2+2mx+nm,n為常數(shù),且m> 0,n>0) ”改為“拋物線My= ax2+2mx+nm,n為常數(shù),且m≠ 0,a≠0, n>0) ”,其他條件不變, 探究 26題中問題.

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  (福建南平2003年中考試題)請寫一個三項(xiàng)式,使它能先提公因式,再運(yùn)用公式來分解.你編寫的三項(xiàng)式是________,分解因式的結(jié)果是________.

 

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