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            • 1.

              \((1)\)若\(\sqrt[3]{0.3670} =0.7160\),\(\sqrt[3]{3.670} =1.542\),则\(\sqrt[3]{3670} =\)_____.

              \((2)\)已知\(\begin{cases}x=2 \\ y=1\end{cases} \)是二元一次方程组\(\begin{cases}mx+ny=7 \\ nx-my=1\end{cases} \)的解,则\(m+3n\)的立方根为_____.

              \((3)\)已知实数\(a\)的立方根是\(4\),则\(\sqrt{a} \)的平方根是_____.

              \((4)\)观察下列各式:\(\sqrt{1+ \dfrac{1}{3}}=2 \sqrt{ \dfrac{1}{3}}, \sqrt{2+ \dfrac{1}{4}}=3 \sqrt{ \dfrac{1}{4}}, \sqrt{3+ \dfrac{1}{5}}=4 \sqrt{ \dfrac{1}{5}}, \),\(…\)请你找出其中规律,并将第\(n(n\geqslant 1)\)个等式写出来_____.

              \((5)\)定义运算“\(*\)”,规定\(x*y=ax^{2}+by\),其中\(a\)、\(b\)为常数,且\(1*2=5\),\(2*1=6\),则\(2*3=\)_____.

              \((6)\)已知\(AM/\!/CN\),点\(B\)为平面内一点,\(AB⊥BC\)于\(B\),过点\(B\)作\(BD⊥AM\)于点\(D\),如图,点\(E\)、\(F\)在\(DM\)上,连接\(BE\)、\(BF\)、\(CF\),若\(BF\)平分\(∠DBC\),\(BE\)平分\(∠ABD\),\(∠FCB+∠NCF=180^{\circ}\),\(∠BFC=3∠DBE\),则\(∠EBC\)的度数为___.

            • 2. 如图,\(Rt\triangle ABC\)中,\(∠C=90^{\circ}\),\(AD\)平分\(∠CAB\),\(DE⊥AB\)于\(E\),若\(AC=6\),\(BC=8\),\(CD=3\).
              \((1)\)求\(DE\)的长;
              \((2)\)求\(\triangle ADB\)的面积.
            • 3.

              如图,\(\triangle ABC\)中,\(∠BAC=90^{\circ}\),\(AD⊥BC\),\(∠ABC\)的平分线\(BE\)交\(AD\)于点\(F\),\(AG\)平分\(∠DAC.\)给出下列结论:\(①∠BAD=∠C\);\(②∠AEF=∠AFE\);\(③∠EBC=∠C\);\(④AG⊥EF.\)其中正确的结论是(    ).


              A.\(②③④\)
              B.\(①③④\)
              C.\(①②④\)
              D.\(①②③\)
            • 4.
              到三角形三边距离相等的点是\((\)  \()\)
              A.三条高的交点
              B.三条中线的交点
              C.三条角平分线的交点
              D.不能确定
            • 5.
              如图,在\(\triangle ABC\)中,\(∠C=90^{\circ}\),\(AC=BC\),\(AD\)平分\(∠CAB\)交\(BC\)于点\(D\),\(DE⊥AB\)于点\(E\),若\(BC=7\),则\(AE\)的长为\((\)  \()\)
              A.\(4\)
              B.\(5\)
              C.\(6\)
              D.\(7\)
            • 6.

              将一幅三角板拼成如图所示的图形,过点\(C\)作\(CF\)平分\(\angle DCE\)交\(DE\)于点\(F\).

              \((1)\)求证:\(CF/\!/AB\).

              \((2)\)求\(\angle DFC\)的度数.

            • 7.

              \(\triangle ABC\)中,\(∠C=90^{\circ}\),\(AD\)平分\(∠BAC\),交\(BC\)于点\(D.\)若\(DC=7\),则\(D\)到\(AB\)的距离是                        

            • 8.

              如图,\(\triangle ABC\)是等腰直角三角形,点\(D\)在\(AC\)边上,\(BD\)平分\(∠ABC\),\(DE⊥BC\)于点\(E\),且\(BC=10cm\),则\(\triangle DCE\)的周长为________\(cm\).

            • 9. 下图(1)、(2)分别是        的展开图.
            • 10. 选项图中有四个正方体,只有一个是如图所示的纸片折叠而成的,请指出是哪一个?(  )
              A.
              B.
              C.
              D.
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