陕西省渭南市大荔县2021-2022学年八年级上学期数学第二次月考试题（有答案）

这是一份陕西省渭南市大荔县2021-2022学年八年级上学期数学第二次月考试题（有答案），共8页。试卷主要包含了本试卷共6页，总分120分，用三角尺可按下面方法画角平分线等内容，欢迎下载使用。
大荔县2021~2022学年度第一学期第二阶段检测八年级数学试题注意事项：1．本试卷共6页，总分120分。考试时间120分钟。2．领到试卷和答题卡后，请用0.5毫米黑色墨水签字笔，分别在试卷和答题卡上填写姓名和准考证号。3．请在答题卡上各题的指定区域内作答，否则作答无效。4．作图时，先用铅笔作图，再用规定签字笔描黑。5．考试结束，本试卷和答题卡一并交回。一、选择题（共8小题，每小题3分，计24分．每小题只有一个选项是符合题意的）1．计算的结果是（    ）A．1 B．0 C． D．22．下列关于体育运动的图形中是轴对称图形的是（    ）A． B． C． D．3．下列各组数可能是一个三角形的三条边长的是（    ）A．3，4，5 B．4，4，9 C．1，2，3 D．2，6，84．如图，，则与相等的角是（    ）A． B． C． D．5．下列运算正确的是（    ）A．  B．C．   D．6．用三角尺可按下面方法画角平分线：已知在两边上分别取，再分别过点M，N作OA，OB的垂线，两垂线交与点P，画射线OP，则OP平分．作图过程用了，那么所用的判定定理是（    ）A．SSS B．AAS C．HL D．ASA7．如图，在中，，，以点B为圆心，BA长为半径画弧，交CB于点T，连接AT，则的度数是（    ）A．15° B．20° C．25° D．30°8．如图，在中，，，且，MN为AC的垂直平分线，设P为直线MN上任一点，则的最小值为（    ）A．1 B．1.5 C．2 D．4二、填空题（共5小题，每小题3分，计15分）9．点关于x轴的对称点的坐标为________．10．一个正多边形的内角和为540°，则它的一个外角等于________°．11．已知能运用完全平方公式分解因式，则m的值为________．12．若，，则________．13．如图，中，，CE为的中线，BD为AC边上的高，BF平分交CE于点G，连接AG交BD于点M，则的度数为________°．三、解答题（共13小题，计81分．解答应写出过程）14．（5分）计算：．15．（5分）分解因式：．16．（5分）如图，点C为的边AB的延长线上一点，过点C作于点E，CE交BF于点G，若，，求的度数．17．（5分）如图，在中，请用尺规作图法作AB的垂直平分线EF，分别交AC、AB于点E、F．（不写作法，保留作图痕迹）18．（5分）如图，和的边BC和EF在一条直线上，且，，．求证：．19．（5分）先化简，再求值：，其中，．20．（5分）如图，在中，，AD平分，于点E，点F在AC上，，连接DF．求证：．21．（6分）如图，在中，，于点D，BF平分交AD于点E，交AC于点F，若，求AE的长．22．（7分）如图，在平面直角坐标系中，已知的三个顶点坐标分别为，，．（1）在图中作出关于y轴对称的；（2）在图中作出关于x轴对称的，并写出点C的对应点的坐标．23．（7分）探究下面的问题：（1）如图甲，在边长为a的正方形中去掉一个边长为b的小正方形（），把余下的部分剪拼成如图乙的一个长方形，通过计算两个图形（阴影部分）的面积，验证了一个等式，这个等式是________（用含a、b的式子表示），即乘法公式中的公式________（填“完全平方”或“平方差”）．（2）运用你所得到的公式计算：．24．（8分）如图，某小区有一块长为（）米，宽为（）米的长方形地块，角上有四个边长均为（）米的小正方形空地，开发商计划将阴影部分进行绿化，用含有a、b的式子表示绿化的总面积．（结果写成最简形式）25．（8分）如图，在中，，，，垂足为G，且，，其两边分别交边AB，AC于点E，F．（1）连接BD，求证：是等边三角形；（2）试猜想：线段AE、AF与AD之间有怎样的数量关系？并给出证明．26．（10分）我们已经学过将一个多项式分解因式的方法有提公因式法和公式法，其实分解因式的方法还有分组分解法、拆项法等等．①分组分解法：将一个多项式适当分组后，可提公因式或运用公式继续分解的方法叫做分组分解法．例如：．②拆项法：将一个多项式的某一项拆成两项后，可提公因式或运用公式继续分解的方法叫做拆项法．例如：．（1）仿照以上方法，按照要求分解因式：①（分组分解法）；②（拆项法）；（2）已知a、b、c为的三条边，且满足，求的周长；（3）已知的三边长a，b，c满足，判断的形状并说明理由． 大荔县2021~2022学年度第一学期第二阶段检测八年级数学试题参考答案及评分标准一、选择题（共8小题，每小题3分，计24分．每小题只有一个选项是符合题意的）1．A    2．D    3．A    4．B    5．D    6．C    7．B    8．C二、填空题（共5小题，每小题3分，计15分）9．    10．72    11．    12．    13．45三、解答题（共13小题，计81分．解答应写出过程）14．解：原式·····································································（3分）．···································································（5分）15．解：··········································································（2分）．·········································································（5分）16．解：在中，，∴，············································································（1分）∴．············································································（3分）∴··············································································（5分）17．解：如图，EF即为所求．·························································（5分）18．证明：∵，∴，∴，············································································（1分）在和中，∴，············································································（3分）∴，∴．············································································（5分）19．解：原式，，，···································································（3分）当，时，原式．···································································（5分）20．证明：AD平分，，，∴，············································································（1分）在和中，∴，············································································（3分）∴．············································································（5分）21．解：∵BF平分，∴．············································································（1分）∵，，∴，∴．············································································（3分）∵，∴，············································································（5分）∴．············································································（6分）22．解：（1）如图，即为所作．······················································（3分）（2）如图，即为所作．·····························································（6分）的坐标为．·······································································（7分）23．解：（1），平方差．····························································（4分）（2）原式．······································································（7分）24．解：根据题意得：················································································（3分）················································································（6分）平方米，答：绿化的面积是（）平方米．·······················································（8分）25．（1）证明：，，∴．············································································（1分）∵，∴．············································································（2分）∵，∴是等边三角形．··································································（4分）（2）．证明：∵是等边三角形，∴，．∴，∴，∴，············································································（5分）在与中，∴，············································································（6分）∴，∴．············································································（8分）26．解：（1）①················································································（1分）．··············································································（2分）②················································································（3分）．··············································································（4分）（2）∵，∴，············································································（5分）∴，∴，，，·········································································（6分）∴．∴的周长为7．····································································（7分）（3），∴，∴，············································································（8分）∴或或且，·······································································（9分）∴或或，∴是等腰三角形或等边三角形．·······················································（10分）