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初中数学八年级上册试题库(555题)




第83题

已知,\(△ABC,△DEF,△XYZ\)的相关数据如图所示,则(  )




A.\(△ABC≌△XYZ\)

B.\(△DEF≌△XYZ\)

C.\(∠C=∠Z\)

D.\(∠F=80°\)


参考答案:C


第84题

如图,线段\(AC\)\(BD\)相交于点\(E\),连接\(AB\)\(CD\),已知\(\angle A = \angle D = 90^\circ \)\(AC = BD\)

求证:\(BE = CE\)

图片 3



参考答案:

证明:连接\(BC\),如图所示:

\(\because \angle A = \angle D = 90^\circ \)

\({\rm{Rt}}\Delta {\rm{ABC}}\)\({\rm{Rt}}\Delta {\rm{DCB}}\)中,

\(\left\{ {\begin{array}{*{20}{l}}
{AC = BD} \\
{BC = CB}
\end{array}} \right.\)

\(\therefore {\rm{Rt}}\Delta ABC \cong {\rm{Rt}}\Delta DCB(HL)\)

\(\therefore AB = DC\)

\(\Delta ABE\)\(\Delta DCE\)中,

\(\left\{ {\begin{array}{*{20}{l}}
\begin{gathered}
\angle A = \angle D \\
\angle AEB = \angle DEC \\
\end{gathered} \\
{AB = DC}
\end{array}} \right.\)

\(\therefore \Delta ABE \cong \Delta DCE(AAS)\)

\(\therefore BE = CE\)

 

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第85题

如图,在\(\Delta ABC\)\(\Delta CDE\)中,\(\angle ACB = \angle CED = 90^\circ \)\(AB = CD\)\(CE = AC\),则下列结论中错误的是\((\)  \()\)


A.\(\Delta ABC \cong \Delta CDE\)

B.\(\angle CAB = \angle DCE\)

C.\(AB \bot CD\)

D.\(E\)为\(BC\)中点


参考答案:D







第91题

如图,在\(3 \times 3\)的方格图中,每个小方格的边长都为1,则\(\angle 1\)\(\angle 2\)的关系是\((\)  \()\)


A.\(\angle 1 = \angle 2\)

B.\(\angle 2 = 2\angle 1\)

C.\(\angle 1 + \angle 2 = 90^\circ \)

D.\(\angle 1 + \angle 2 = 180^\circ \)


参考答案:D




第94题

如图,四边形\(ABCD\)中,\(\angle B + \angle D = 180^\circ \)\(\angle BCD = 150^\circ \)\(CB = CD\)\(M\)\(N\)\(AB\)\(AD\)上的两个动点,且\(\angle MCN = 75^\circ \)。求证:\(MN = BM + DN\)





参考答案:见解析


解析:


证明:延长\(AB\)至点\(E\),使得\(BE = DN\),连接\(CE\)



\(\because \)四边形\(ABCD\)中,\(\angle B + \angle D = 180^\circ \)\(\angle ABC + \angle CBE = 180^\circ \)



\(\therefore \angle CBE = \angle CDN\)



\(\Delta CBE\)\(\Delta CDN\)中,



\(\left\{ {\begin{array}{*{20}{l}} {CB = CD} \\\ {\angle CBE = \angle CDN} \\\ {BE = DN} \end{array}} \right.\)



\(\therefore \Delta CBE \cong \Delta CDN(SAS)\)



\(\therefore \angle BCE = \angle DCN\)\(CN = CE\)



\(\because \angle BCD = 150^\circ \)\(\angle MCN = 75^\circ \)



\(\therefore \angle MCE = \angle MCB + \angle BCE = \angle MCB + \angle DCN = 75^\circ \)



\(\therefore \angle MCN = \angle MCE\)



\(\Delta ECM\)\(\Delta NCM\)中,



\(\left\{ {\begin{array}{*{20}{l}} {MC = MC} \\\ {\angle MCN = \angle MCE} \\\ {CN = CE} \end{array}} \right.\)



\(\therefore \Delta ECM \cong \Delta NCM(SAS)\)



\(\therefore MN = ME = BM + BE = BM + DN\)









第99题

如图,在\(\Delta ABC\)中,点\(D\)在射线\(BC\)上,过\(AC\)的中点\(E\)作线段\(FG\)\(AB\)于点\(G\),连接\(CF\),且\(\angle B = \angle DCF\)\(CF = 6\)\(AC = BC = 10\)\(AG = 3BG\),求\(\Delta ABC\)的周长。



参考答案:证明:\(\because \angle B = \angle DCF\),\(\therefore CF//AB\),\(\therefore \angle FCA = \angle A\),\(\angle F = \angle FGA\),\(\because \)点\(E\)是\(AC\)的中点,\(\therefore AE = EC\),在\(\Delta AEG\)和\(\Delta CEF\)中,\(\left\{ {\begin{array}{*{20}{l}}
{\angle A = \angle FCA} \\
{\angle FGA = \angle F} \\
{AE = EC}
\end{array}} \right.\),\(\therefore \Delta AEG \cong \Delta CEF(AAS)\)。\(\because \Delta AEG \cong \Delta CEF\);\(\therefore CF = AG = 6\),\(\because AG = 3BG\),\(\therefore BG = 2\),\(\therefore AB = 8\),\(\therefore \Delta ABC\)的周长\( = AB + AC + BC = 28\)。


第100题

如图:在\(\Delta ABC\)中,\(BE\)\(CF\)分别是\(AC\)\(AB\)两边上的高,在\(BE\)上截取\(BD = AC\),在

\(CF\)的延长线上截取\(CG = AB\),连接\(AD\)\(AG\)。观察线段\(AD\)\(AG\)有什么关系,并说明

理由。



参考答案:线段\(AD\)与\(AG\)垂直且相等\(\because BE \bot AC\),\(CF \bot AB\),\(\therefore \angle HFB = \angle HEC = 90^\circ \),又\(\because \angle BHF = \angle CHE\),\(\therefore \angle ABD = \angle ACG\),在\(\Delta ABD\)和\(\Delta GCA\)中\(\left\{ {\begin{array}{*{20}{l}}
{AB = CG} \\
{\angle ABD = \angle ACG} \\
{BD = CA}
\end{array}} \right.\),\(\therefore \Delta ABD \cong \Delta GCA(SAS)\),\(\therefore AD = GA\)(全等三角形的对应边相等);\(\because \Delta ABD \cong \Delta GCA\),\(\therefore \angle ADB = \angle GAC\),又\(\because \angle ADB = \angle AED + \angle DAE\),\(\angle GAC = \angle GAD + \angle DAE\),\(\therefore \angle AED = \angle GAD = 90^\circ \),\(\therefore AD \bot GA\)。


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