專題19圖形的平移翻折對(duì)稱（30題）一、單選題1．（2023·四川南充·統(tǒng)考中考真題）如圖，將SKIPIF1<0沿SKIPIF1<0向右平移得到SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的長是（

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A．2 B．SKIPIF1<0 C．3 D．52．（2023·山東·統(tǒng)考中考真題）如圖，四邊形SKIPIF1<0是一張矩形紙片．將其按如圖所示的方式折疊：使SKIPIF1<0邊落在SKIPIF1<0邊上，點(diǎn)SKIPIF1<0落在點(diǎn)SKIPIF1<0處，折痕為SKIPIF1<0；使SKIPIF1<0邊落在SKIPIF1<0邊上，點(diǎn)SKIPIF1<0落在點(diǎn)SKIPIF1<0處，折痕為SKIPIF1<0．若矩形SKIPIF1<0與原矩形SKIPIF1<0相似，SKIPIF1<0，則SKIPIF1<0的長為（）

A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2023·內(nèi)蒙古赤峰·統(tǒng)考中考真題）如圖，在SKIPIF1<0中，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0．點(diǎn)F是SKIPIF1<0中點(diǎn)，連接SKIPIF1<0，把線段SKIPIF1<0沿射線SKIPIF1<0方向平移到SKIPIF1<0，點(diǎn)D在SKIPIF1<0上．則線段SKIPIF1<0在平移過程中掃過區(qū)域形成的四邊形SKIPIF1<0的周長和面積分別是(

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A．16，6 B．18，18 C．16.12 D．12，164．（2023·黑龍江·統(tǒng)考中考真題）如圖，在平面直角坐標(biāo)中，矩形SKIPIF1<0的邊SKIPIF1<0，將矩形SKIPIF1<0沿直線SKIPIF1<0折疊到如圖所示的位置，線段SKIPIF1<0恰好經(jīng)過點(diǎn)SKIPIF1<0，點(diǎn)SKIPIF1<0落在SKIPIF1<0軸的點(diǎn)SKIPIF1<0位置，點(diǎn)SKIPIF1<0的坐標(biāo)是（

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A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2023·浙江嘉興·統(tǒng)考中考真題）如圖，已知矩形紙片SKIPIF1<0，其中SKIPIF1<0，現(xiàn)將紙片進(jìn)行如下操作：第一步，如圖①將紙片對(duì)折，使SKIPIF1<0與SKIPIF1<0重合，折痕為SKIPIF1<0，展開后如圖②；第二步，再將圖②中的紙片沿對(duì)角線SKIPIF1<0折疊，展開后如圖③；第三步，將圖③中的紙片沿過點(diǎn)SKIPIF1<0的直線折疊，使點(diǎn)SKIPIF1<0落在對(duì)角線SKIPIF1<0上的點(diǎn)SKIPIF1<0處，如圖④．則SKIPIF1<0的長為（）

A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2023·甘肅武威·統(tǒng)考中考真題）如圖，將矩形SKIPIF1<0對(duì)折，使邊SKIPIF1<0與SKIPIF1<0，SKIPIF1<0與SKIPIF1<0分別重合，展開后得到四邊形SKIPIF1<0．若SKIPIF1<0，SKIPIF1<0，則四邊形SKIPIF1<0的面積為（

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A．2 B．4 C．5 D．67．（2023·內(nèi)蒙古赤峰·統(tǒng)考中考真題）如圖，把一個(gè)邊長為5的菱形SKIPIF1<0沿著直線SKIPIF1<0折疊，使點(diǎn)C與SKIPIF1<0延長線上的點(diǎn)Q重合．SKIPIF1<0交SKIPIF1<0于點(diǎn)F，交SKIPIF1<0延長線于點(diǎn)E．SKIPIF1<0交SKIPIF1<0于點(diǎn)P，SKIPIF1<0于點(diǎn)M，SKIPIF1<0，則下列結(jié)論，①SKIPIF1<0，②SKIPIF1<0，③SKIPIF1<0，④SKIPIF1<0．正確的是（

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A．①②③ B．②④ C．①③④ D．①②③④二、填空題8．（2023·吉林長春·統(tǒng)考中考真題）如圖，將正五邊形紙片SKIPIF1<0折疊，使點(diǎn)SKIPIF1<0與點(diǎn)SKIPIF1<0重合，折痕為SKIPIF1<0，展開后，再將紙片折疊，使邊SKIPIF1<0落在線段SKIPIF1<0上，點(diǎn)SKIPIF1<0的對(duì)應(yīng)點(diǎn)為點(diǎn)SKIPIF1<0，折痕為SKIPIF1<0，則SKIPIF1<0的大小為__________度．

9．（2023·全國·統(tǒng)考中考真題）如圖，在SKIPIF1<0中，SKIPIF1<0．點(diǎn)SKIPIF1<0，SKIPIF1<0分別在邊SKIPIF1<0，SKIPIF1<0上，連接SKIPIF1<0，將SKIPIF1<0沿SKIPIF1<0折疊，點(diǎn)SKIPIF1<0的對(duì)應(yīng)點(diǎn)為點(diǎn)SKIPIF1<0．若點(diǎn)SKIPIF1<0剛好落在邊SKIPIF1<0上，SKIPIF1<0，則SKIPIF1<0的長為__________．

10．（2023·湖北宜昌·統(tǒng)考中考真題）如圖，小宇將一張平行四邊形紙片折疊，使點(diǎn)SKIPIF1<0落在長邊SKIPIF1<0上的點(diǎn)SKIPIF1<0處，并得到折痕SKIPIF1<0，小宇測(cè)得長邊SKIPIF1<0，則四邊形SKIPIF1<0的周長為_________．

11．（2023·遼寧·統(tǒng)考中考真題）如圖，在三角形紙片SKIPIF1<0中，SKIPIF1<0，點(diǎn)SKIPIF1<0是邊SKIPIF1<0上的動(dòng)點(diǎn)，將三角形紙片沿SKIPIF1<0對(duì)折，使點(diǎn)SKIPIF1<0落在點(diǎn)SKIPIF1<0處，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0的度數(shù)為___________．

12．（2023·江蘇徐州·統(tǒng)考中考真題）如圖，在SKIPIF1<0中，SKIPIF1<0，點(diǎn)SKIPIF1<0在邊SKIPIF1<0上．將SKIPIF1<0沿SKIPIF1<0折疊，使點(diǎn)SKIPIF1<0落在點(diǎn)SKIPIF1<0處，連接SKIPIF1<0，則SKIPIF1<0的最小值為_______．

13．（2023·黑龍江齊齊哈爾·統(tǒng)考中考真題）矩形紙片SKIPIF1<0中，SKIPIF1<0，SKIPIF1<0，點(diǎn)SKIPIF1<0在SKIPIF1<0邊所在的直線上，且SKIPIF1<0，將矩形紙片SKIPIF1<0折疊，使點(diǎn)SKIPIF1<0與點(diǎn)SKIPIF1<0重合，折痕與SKIPIF1<0，SKIPIF1<0分別交于點(diǎn)SKIPIF1<0，SKIPIF1<0，則線段SKIPIF1<0的長度為______．14．（2023·四川涼山·統(tǒng)考中考真題）如圖，在SKIPIF1<0紙片中，SKIPIF1<0，SKIPIF1<0是SKIPIF1<0邊上的中線，將SKIPIF1<0沿SKIPIF1<0折疊，當(dāng)點(diǎn)SKIPIF1<0落在點(diǎn)SKIPIF1<0處時(shí)，恰好SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0_________．

15．（2023·新疆·統(tǒng)考中考真題）如圖，在SKIPIF1<0中，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，點(diǎn)SKIPIF1<0是SKIPIF1<0上一動(dòng)點(diǎn)，將SKIPIF1<0沿SKIPIF1<0折疊得到SKIPIF1<0，當(dāng)點(diǎn)SKIPIF1<0恰好落在SKIPIF1<0上時(shí)，SKIPIF1<0的長為______．

16．（2023·江蘇揚(yáng)州·統(tǒng)考中考真題）如圖，已知正方形SKIPIF1<0的邊長為1，點(diǎn)E、F分別在邊SKIPIF1<0上，將正方形沿著SKIPIF1<0翻折，點(diǎn)B恰好落在SKIPIF1<0邊上的點(diǎn)SKIPIF1<0處，如果四邊形SKIPIF1<0與四邊形SKIPIF1<0的面積比為3∶5，那么線段SKIPIF1<0的長為________．

17．（2023·湖北隨州·統(tǒng)考中考真題）如圖，在矩形SKIPIF1<0中，SKIPIF1<0，M是邊SKIPIF1<0上一動(dòng)點(diǎn)（不含端點(diǎn)），將SKIPIF1<0沿直線SKIPIF1<0對(duì)折，得到SKIPIF1<0．當(dāng)射線SKIPIF1<0交線段SKIPIF1<0于點(diǎn)P時(shí)，連接SKIPIF1<0，則SKIPIF1<0的面積為___________；SKIPIF1<0的最大值為___________．

18．（2023·湖南·統(tǒng)考中考真題）如圖，在矩形SKIPIF1<0中，SKIPIF1<0，動(dòng)點(diǎn)SKIPIF1<0在矩形的邊上沿SKIPIF1<0運(yùn)動(dòng)．當(dāng)點(diǎn)SKIPIF1<0不與點(diǎn)SKIPIF1<0重合時(shí)，將SKIPIF1<0沿SKIPIF1<0對(duì)折，得到SKIPIF1<0，連接SKIPIF1<0，則在點(diǎn)SKIPIF1<0的運(yùn)動(dòng)過程中，線段SKIPIF1<0的最小值為__________．

19．（2023·湖北武漢·統(tǒng)考中考真題）如圖，SKIPIF1<0平分等邊SKIPIF1<0的面積，折疊SKIPIF1<0得到SKIPIF1<0分別與SKIPIF1<0相交于SKIPIF1<0兩點(diǎn)．若SKIPIF1<0，用含SKIPIF1<0的式子表示SKIPIF1<0的長是________．

20．（2023·廣東深圳·統(tǒng)考中考真題）如圖，在SKIPIF1<0中，SKIPIF1<0，SKIPIF1<0，點(diǎn)D為SKIPIF1<0上一動(dòng)點(diǎn)，連接SKIPIF1<0，將SKIPIF1<0沿SKIPIF1<0翻折得到SKIPIF1<0，SKIPIF1<0交SKIPIF1<0于點(diǎn)G，SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0______．

21．（2023·黑龍江·統(tǒng)考中考真題）矩形SKIPIF1<0中，SKIPIF1<0，將矩形SKIPIF1<0沿過點(diǎn)SKIPIF1<0的直線折疊，使點(diǎn)SKIPIF1<0落在點(diǎn)SKIPIF1<0處，若SKIPIF1<0是直角三角形，則點(diǎn)SKIPIF1<0到直線SKIPIF1<0的距離是__________．22．（2023·四川成都·統(tǒng)考中考真題）如圖，在SKIPIF1<0中，SKIPIF1<0，SKIPIF1<0平分SKIPIF1<0交SKIPIF1<0于點(diǎn)SKIPIF1<0，過SKIPIF1<0作SKIPIF1<0交SKIPIF1<0于點(diǎn)SKIPIF1<0，將SKIPIF1<0沿SKIPIF1<0折疊得到SKIPIF1<0，SKIPIF1<0交SKIPIF1<0于點(diǎn)SKIPIF1<0．若SKIPIF1<0，則SKIPIF1<0__________．

23．（2023·四川南充·統(tǒng)考中考真題）如圖，在等邊SKIPIF1<0中，過點(diǎn)C作射線SKIPIF1<0，點(diǎn)M，N分別在邊SKIPIF1<0，SKIPIF1<0上，將SKIPIF1<0沿SKIPIF1<0折疊，使點(diǎn)B落在射線SKIPIF1<0上的點(diǎn)SKIPIF1<0處，連接SKIPIF1<0，已知SKIPIF1<0．給出下列四個(gè)結(jié)論：①SKIPIF1<0為定值；②當(dāng)SKIPIF1<0時(shí)，四邊形SKIPIF1<0為菱形；③當(dāng)點(diǎn)N與C重合時(shí)，SKIPIF1<0；④當(dāng)SKIPIF1<0最短時(shí)，SKIPIF1<0．其中正確的結(jié)論是________（填寫序號(hào)）24．（2023·浙江杭州·統(tǒng)考中考真題）如圖，在SKIPIF1<0中，SKIPIF1<0，點(diǎn)SKIPIF1<0分別在邊SKIPIF1<0，SKIPIF1<0上，連接SKIPIF1<0，已知點(diǎn)SKIPIF1<0和點(diǎn)SKIPIF1<0關(guān)于直線SKIPIF1<0對(duì)稱．設(shè)SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0_________（結(jié)果用含SKIPIF1<0的代數(shù)式表示）．

三、解答題25．（2023·安徽·統(tǒng)考中考真題）如圖，在由邊長為1個(gè)單位長度的小正方形組成的網(wǎng)格中，點(diǎn)SKIPIF1<0均為格點(diǎn)（網(wǎng)格線的交點(diǎn)）．

(1)畫出線段SKIPIF1<0關(guān)于直線SKIPIF1<0對(duì)稱的線段SKIPIF1<0；(2)將線段SKIPIF1<0向左平移2個(gè)單位長度，再向上平移1個(gè)單位長度，得到線段SKIPIF1<0，畫出線段SKIPIF1<0；(3)描出線段SKIPIF1<0上的點(diǎn)SKIPIF1<0及直線SKIPIF1<0上的點(diǎn)SKIPIF1<0，使得直線SKIPIF1<0垂直平分SKIPIF1<0．26．（2023·四川廣安·統(tǒng)考中考真題）將邊長為2的正方形剪成四個(gè)全等的直角三角形，用這四個(gè)直角三角形拼成符合要求的四邊形，請(qǐng)?jiān)谙铝芯W(wǎng)格中畫出你拼成的四邊形（注：①網(wǎng)格中每個(gè)小正方形的邊長為1；②所拼的圖形不得與原圖形相同；③四邊形的各頂點(diǎn)都在格點(diǎn)上）．

27．（2023·內(nèi)蒙古通遼·統(tǒng)考中考真題）綜合與實(shí)踐課上，老師讓同學(xué)們以“正方形的折疊”為主題開展數(shù)學(xué)活動(dòng)，有一位同學(xué)操作過程如下：操作一：對(duì)折正方形紙片SKIPIF1<0，使SKIPIF1<0與SKIPIF1<0重合，得到折痕SKIPIF1<0，把紙片展平；操作二：在SKIPIF1<0上選一點(diǎn)P，沿SKIPIF1<0折疊，使點(diǎn)A落在正方形內(nèi)部點(diǎn)M處，把紙片展平，連接SKIPIF1<0、SKIPIF1<0，延長SKIPIF1<0交SKIPIF1<0于點(diǎn)Q，連接SKIPIF1<0．

(1)如圖1，當(dāng)點(diǎn)M在SKIPIF1<0上時(shí)，SKIPIF1<0___________度；(2)改變點(diǎn)P在SKIPIF1<0上的位置（點(diǎn)P不與點(diǎn)A，D重合）如圖2，判斷SKIPIF1<0與SKIPIF1<0的數(shù)量關(guān)系，并說明理由．28．（2023·湖北·統(tǒng)考中考真題）如圖，將邊長為3的正方形SKIPIF1<0沿直線SKIPIF1<0折疊，使點(diǎn)SKIPIF1<0的對(duì)應(yīng)點(diǎn)SKIPIF1<0落在邊SKIPIF1<0上（點(diǎn)SKIPIF1<0不與點(diǎn)SKIPIF1<0重合），點(diǎn)SKIPIF1<0落在點(diǎn)SKIPIF1<0處，SKIPIF1<0與SKIPIF1<0交于點(diǎn)SKIPIF1<0，折痕分別與邊SKIPIF1<0，SKIPIF1<0交于點(diǎn)SKIPIF1<0，連接SKIPIF1<0．

(1)求證：SKIPIF1<0；(2)若SKIPIF1<0，求SKIPI