中考數(shù)學(xué)一輪復(fù)習(xí)提升練習(xí)第4章 三角形真題測(cè)試（提升卷）（原卷版）

第三章三角形章節(jié)測(cè)試(時(shí)間：90分鐘滿(mǎn)分：120分)一、選擇題（本大題共10小題，每小題3分，共30分．在每小題給出的四個(gè)選項(xiàng)中，只有一個(gè)選項(xiàng)是符合題目要求的）1．（2023·吉林長(zhǎng)春·統(tǒng)考中考真題）如圖，用直尺和圓規(guī)作SKIPIF1<0的角平分線(xiàn)，根據(jù)作圖痕跡，下列結(jié)論不一定正確的是（

）

A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2023·四川宜賓·統(tǒng)考中考真題）如圖，SKIPIF1<0，且SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0等于（）

A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2023·北京·統(tǒng)考中考真題）如圖，點(diǎn)A、B、C在同一條線(xiàn)上，點(diǎn)B在點(diǎn)A，C之間，點(diǎn)D，E在直線(xiàn)AC同側(cè)，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，連接DE，設(shè)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，給出下面三個(gè)結(jié)論：①SKIPIF1<0；②SKIPIF1<0；③SKIPIF1<0；

上述結(jié)論中，所有正確結(jié)論的序號(hào)是（

）A．①② B．①③ C．②③ D．①②③4．（2023·四川遂寧·統(tǒng)考中考真題）在方格圖中，以格點(diǎn)為頂點(diǎn)的三角形叫做格點(diǎn)三角形．在如圖所示的平面直角坐標(biāo)系中，格點(diǎn)SKIPIF1<0成位似關(guān)系，則位似中心的坐標(biāo)為（

）

A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2023·內(nèi)蒙古·統(tǒng)考中考真題）如圖，直線(xiàn)SKIPIF1<0，直線(xiàn)SKIPIF1<0與直線(xiàn)SKIPIF1<0分別相交于點(diǎn)SKIPIF1<0，點(diǎn)SKIPIF1<0在直線(xiàn)SKIPIF1<0上，且SKIPIF1<0．若SKIPIF1<0，則SKIPIF1<0的度數(shù)為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2023·山西·統(tǒng)考中考真題）如圖，一束平行于主光軸的光線(xiàn)經(jīng)凸透鏡折射后，其折射光線(xiàn)與一束經(jīng)過(guò)光心SKIPIF1<0的光線(xiàn)相交于點(diǎn)SKIPIF1<0，點(diǎn)SKIPIF1<0為焦點(diǎn)．若SKIPIF1<0，則SKIPIF1<0的度數(shù)為（

）

A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．（2023·江蘇無(wú)錫·統(tǒng)考中考真題）如圖SKIPIF1<0中，SKIPIF1<0，SKIPIF1<0為SKIPIF1<0中點(diǎn)，若點(diǎn)SKIPIF1<0為直線(xiàn)SKIPIF1<0下方一點(diǎn)，且SKIPIF1<0與SKIPIF1<0相似，則下列結(jié)論：①若SKIPIF1<0，SKIPIF1<0與SKIPIF1<0相交于SKIPIF1<0，則點(diǎn)SKIPIF1<0不一定是SKIPIF1<0的重心；②若SKIPIF1<0，則SKIPIF1<0的最大值為SKIPIF1<0；③若SKIPIF1<0，則SKIPIF1<0的長(zhǎng)為SKIPIF1<0；④若SKIPIF1<0，則當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0取得最大值．其中正確的為（

）

A．①④ B．②③ C．①②④ D．①③④8．（2023·安徽·統(tǒng)考中考真題）如圖，點(diǎn)SKIPIF1<0在正方形SKIPIF1<0的對(duì)角線(xiàn)SKIPIF1<0上，SKIPIF1<0于點(diǎn)SKIPIF1<0，連接SKIPIF1<0并延長(zhǎng)，交邊SKIPIF1<0于點(diǎn)SKIPIF1<0，交邊SKIPIF1<0的延長(zhǎng)線(xiàn)于點(diǎn)SKIPIF1<0．若SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0（

）

A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．（2023·四川眉山·統(tǒng)考中考真題）如圖，在正方形SKIPIF1<0中，點(diǎn)E是SKIPIF1<0上一點(diǎn)，延長(zhǎng)SKIPIF1<0至點(diǎn)F，使SKIPIF1<0，連結(jié)SKIPIF1<0，SKIPIF1<0交SKIPIF1<0于點(diǎn)K，過(guò)點(diǎn)A作SKIPIF1<0，垂足為點(diǎn)H，交SKIPIF1<0于點(diǎn)G，連結(jié)SKIPIF1<0．下列四個(gè)結(jié)論：①SKIPIF1<0；②SKIPIF1<0；③SKIPIF1<0；④SKIPIF1<0．其中正確結(jié)論的個(gè)數(shù)為（

）

A．1個(gè) B．2個(gè) C．3個(gè) D．4個(gè)10．（2023·湖北黃岡·統(tǒng)考中考真題）如圖，矩形SKIPIF1<0中，SKIPIF1<0，以點(diǎn)B為圓心，適當(dāng)長(zhǎng)為半徑畫(huà)弧，分別交SKIPIF1<0，SKIPIF1<0于點(diǎn)E，F(xiàn)，再分別以點(diǎn)E，F(xiàn)為圓心，大于SKIPIF1<0長(zhǎng)為半徑畫(huà)弧交于點(diǎn)P，作射線(xiàn)SKIPIF1<0，過(guò)點(diǎn)C作SKIPIF1<0的垂線(xiàn)分別交SKIPIF1<0于點(diǎn)M，N，則SKIPIF1<0的長(zhǎng)為（

）

A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．4二、填空題（本大題共10小題，每小題3分，共30分）11．（2023·內(nèi)蒙古通遼·統(tǒng)考中考真題）將一副三角尺如圖所示放置，其中SKIPIF1<0，則SKIPIF1<0___________度．

12．（2023·浙江金華·統(tǒng)考中考真題）如圖，把兩根鋼條SKIPIF1<0的一個(gè)端點(diǎn)連在一起，點(diǎn)SKIPIF1<0分別是SKIPIF1<0的中點(diǎn)．若SKIPIF1<0，則該工件內(nèi)槽寬SKIPIF1<0的長(zhǎng)為_(kāi)_________SKIPIF1<0．

13．（2023·天津·統(tǒng)考中考真題）如圖，在邊長(zhǎng)為3的正方形SKIPIF1<0的外側(cè)，作等腰三角形SKIPIF1<0，SKIPIF1<0．

（1）SKIPIF1<0的面積為_(kāi)_______；（2）若F為SKIPIF1<0的中點(diǎn)，連接SKIPIF1<0并延長(zhǎng)，與SKIPIF1<0相交于點(diǎn)G，則SKIPIF1<0的長(zhǎng)為_(kāi)_______．14．（2023·吉林長(zhǎng)春·統(tǒng)考中考真題）如圖，SKIPIF1<0和SKIPIF1<0是以點(diǎn)SKIPIF1<0為位似中心的位似圖形，點(diǎn)SKIPIF1<0在線(xiàn)段SKIPIF1<0上．若SKIPIF1<0，則SKIPIF1<0和SKIPIF1<0的周長(zhǎng)之比為_(kāi)_________．

15．（2023·四川成都·統(tǒng)考中考真題）如圖，在SKIPIF1<0中，SKIPIF1<0是邊SKIPIF1<0上一點(diǎn)，按以下步驟作圖：①以點(diǎn)SKIPIF1<0為圓心，以適當(dāng)長(zhǎng)為半徑作弧，分別交SKIPIF1<0，SKIPIF1<0于點(diǎn)SKIPIF1<0，SKIPIF1<0；②以點(diǎn)SKIPIF1<0為圓心，以SKIPIF1<0長(zhǎng)為半徑作弧，交SKIPIF1<0于點(diǎn)SKIPIF1<0；③以點(diǎn)SKIPIF1<0為圓心，以SKIPIF1<0長(zhǎng)為半徑作弧，在SKIPIF1<0內(nèi)部交前面的弧于點(diǎn)SKIPIF1<0：④過(guò)點(diǎn)SKIPIF1<0作射線(xiàn)SKIPIF1<0交SKIPIF1<0于點(diǎn)SKIPIF1<0．若SKIPIF1<0與四邊形SKIPIF1<0的面積比為SKIPIF1<0，則SKIPIF1<0的值為_(kāi)__________．

16．（2023·安徽·統(tǒng)考中考真題）清初數(shù)學(xué)家梅文鼎在著作《平三角舉要》中，對(duì)南宋數(shù)學(xué)家秦九韶提出的計(jì)算三角形面積的“三斜求積術(shù)”給出了一個(gè)完整的證明，證明過(guò)程中創(chuàng)造性地設(shè)計(jì)直角三角形，得出了一個(gè)結(jié)論：如圖，SKIPIF1<0是銳角SKIPIF1<0的高，則SKIPIF1<0．當(dāng)SKIPIF1<0，SKIPIF1<0時(shí)，SKIPIF1<0____．

17．（2023·湖北·統(tǒng)考中考真題）如圖，SKIPIF1<0和SKIPIF1<0都是等腰直角三角形，SKIPIF1<0，點(diǎn)SKIPIF1<0在SKIPIF1<0內(nèi)，SKIPIF1<0，連接SKIPIF1<0交SKIPIF1<0于點(diǎn)SKIPIF1<0交SKIPIF1<0于點(diǎn)SKIPIF1<0，連接SKIPIF1<0．給出下面四個(gè)結(jié)論：①SKIPIF1<0；②SKIPIF1<0；③SKIPIF1<0；④SKIPIF1<0．其中所有正確結(jié)論的序號(hào)是_________．18．（2023·內(nèi)蒙古·統(tǒng)考中考真題）如圖，在SKIPIF1<0中，SKIPIF1<0，將SKIPIF1<0繞點(diǎn)A逆時(shí)針?lè)较蛐D(zhuǎn)SKIPIF1<0，得到SKIPIF1<0．連接SKIPIF1<0，交SKIPIF1<0于點(diǎn)D，則SKIPIF1<0的值為_(kāi)_______．

19．（2023·山東日照·統(tǒng)考中考真題）如圖，矩形SKIPIF1<0中，SKIPIF1<0，點(diǎn)P在對(duì)角線(xiàn)SKIPIF1<0上，過(guò)點(diǎn)P作SKIPIF1<0，交邊SKIPIF1<0于點(diǎn)M，N，過(guò)點(diǎn)M作SKIPIF1<0交SKIPIF1<0于點(diǎn)E，連接SKIPIF1<0．下列結(jié)論：①SKIPIF1<0；②四邊形SKIPIF1<0的面積不變；③當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0；④SKIPIF1<0的最小值是20．其中所有正確結(jié)論的序號(hào)是__________．

20．（2023·湖北隨州·統(tǒng)考中考真題）如圖，在SKIPIF1<0中，SKIPIF1<0，D為AC上一點(diǎn)，若SKIPIF1<0是SKIPIF1<0的角平分線(xiàn)，則SKIPIF1<0___________．

三、解答題（本大題共8小題，共66分．解答應(yīng)寫(xiě)出文字說(shuō)明、證明過(guò)程或演算步驟）21．（2023·江蘇蘇州·統(tǒng)考中考真題）如圖，在SKIPIF1<0中，SKIPIF1<0為SKIPIF1<0的角平分線(xiàn)．以點(diǎn)SKIPIF1<0圓心，SKIPIF1<0長(zhǎng)為半徑畫(huà)弧，與SKIPIF1<0分別交于點(diǎn)SKIPIF1<0，連接SKIPIF1<0．

(1)求證：SKIPIF1<0；(2)若SKIPIF1<0，求SKIPIF1<0的度數(shù)．22．（2023·云南·統(tǒng)考中考真題）如圖，SKIPIF1<0是SKIPIF1<0的中點(diǎn)，SKIPIF1<0．求證：SKIPIF1<0．

23．（2023·湖南·統(tǒng)考中考真題）如圖，SKIPIF1<0，點(diǎn)SKIPIF1<0是線(xiàn)段SKIPIF1<0上的一點(diǎn)，且SKIPIF1<0．已知SKIPIF1<0．

(1)證明：SKIPIF1<0．(2)求線(xiàn)段SKIPIF1<0的長(zhǎng)．24．（2023·四川涼山·統(tǒng)考中考真題）如圖，在SKIPIF1<0中，對(duì)角線(xiàn)SKIPIF1<0與SKIPIF1<0相交于點(diǎn)SKIPIF1<0，SKIPIF1<0，過(guò)點(diǎn)SKIPIF1<0作SKIPIF1<0交SKIPIF1<0于點(diǎn)SKIPIF1<0．

(1)求證：SKIPIF1<0；(2)若SKIPIF1<0，SKIPIF1<0，求SKIPIF1<0的長(zhǎng)．25．（2023·上?！そy(tǒng)考中考真題）如圖，在梯形SKIPIF1<0中SKIPIF1<0，點(diǎn)F，E分別在線(xiàn)段SKIPIF1<0，SKIPIF1<0上，且SKIPIF1<0，SKIPIF1<0

(1)求證：SKIPIF1<0(2)若SKIPIF1<0，求證：SKIPIF1<026．（2023·四川宜賓·統(tǒng)考中考真題）渝昆高速鐵路的建成，將會(huì)顯著提升宜賓的交通地位．渝昆高速鐵路宜賓臨港長(zhǎng)江公鐵兩用大橋（如圖SKIPIF1<0），橋面采用國(guó)內(nèi)首創(chuàng)的公鐵平層設(shè)計(jì)．為測(cè)量左橋墩底到橋面的距離SKIPIF1<0，如圖SKIPIF1<0．在橋面上點(diǎn)SKIPIF1<0處，測(cè)得SKIPIF1<0到左橋墩SKIPIF1<0的距離SKIPIF1<0米，左橋墩所在塔頂SKIPIF1<0的仰角SKIPIF1<0