初三数学讲义(6)相似三角形的B字型

专业好文档初三数学讲义（6）相似专题二B字型相似 姓名 引例 已知：如图，在正方形ABCD中，Q是边CD上的一点, QPAQ交 BC于Q,.求证：ADQ与QCP相似。ADCPB601、 如图，已知P是等边的边上一点，为上一点，若。求证：ABPPCD。2、 如图,在等腰ABC中, BAC=90,点D是BC边上的一个动点(不与B、C重合），在AC上取一点E，使ADE=45. 求证：ABDDCE。解题总结：1）请根据三道例题归纳出一个相似基本图形：练习1.如图, 边长为4的正方形ABCD中, P是边BC上的一点, QPAP交 DC于Q, 设 BP= x, ADQ的面积为y.(1) 求y与x之间的函数关系式,并求自变量x的取值范围;(2) 问P点在何位置时,ADQ的面积最小?最小面积是多少?练习2.如图，梯形ABCD中 ADBC ，ABC=90，AD=9，BC=12，AB=10，在线段BC上任取一点P，作射线PEPD，与线段AB交于点E.（1）试确定CP=5时点E的位置；（2）若设CP=x，BE=y，试写出y关于自变量x的函数关系式，并求出自变量x的取值范围.练习3.矩形ABCD中，把DA沿AF对折，使D与CB边上的点E重合，若AD=10, AB= 8,则EF=_练习4.在直角梯形ABCF中，CB=14，CF=4, AB=6,CFAB,在边CB上找一点E,使以E、A、B为顶点的三角形和以E、C、F为顶点的三角形相似，则CE= 练习5.如图，点A在反比例函数的图像上,点B在反比例函数(k<0)的图像上,且AOB=90，tanOAB=4:3，则k的值是 练习6.如图,在等腰ABC中, BAC=90,AB=AC=1,点D是BC边上的一个动点(不与B、C重合），在AC上取一点E，使ADE=45.（1）求证：ABDDCE；（2）设BD=x，AE=y，求y关于x的函数关系式及自变量x的取值范围，并求出当BD为何值时AE取得最小值；（3）当ADE是等腰三角形时，求AE的长。练习7.在平面直角坐标系中，抛物线与轴的两交点分别为A（-3，0）、B（1，0），过顶点C作CHx轴于点H.（1）直接填写：= ，b= ，顶点C的坐标为 ；（2）在轴上是否存在点D，使得ACD是以AC为斜边的直角三角形？若存在，求出点D的坐标；若不存在，说明理由；.练习8.如图，在矩形ABCD中，AB4，AD10一把三角尺的直角顶点P在AD上滑动时（点P与A、D不重合），一直角边始终经过点C，另一直角边与AB交于点E（1）证明DPCAEP；（2）当CPD30时，求AE的长；（3）是否存在这样的点P，使DPC的周长等于AEP周长的倍？若存在，求出DP的长；若不存在，请说明理由练习9.如图，已知抛物线与x轴交于A（2，0）、B（6，0）两点，与y轴交于点C（0，3）.（1）求此抛物线的解析式；（2）抛物线上有一点P，满足以PC为直径的圆交抛物线与点B，求点P的坐标；（3）在（2）的条件下，问在y轴上是否存在点E，使得以A、O、E为顶点的三角形与PBC相似？若存在，求出点E的坐标；若不存在，请说明理由.练习10.(2011湖南)孔明是一个喜欢探究钻研的同学，他在和同学们一起研究某条抛物线的性质时，将一把直角三角板的直角顶点置于平面直角坐标系的原点，两直角边与该抛物线交于、两点，请解答以下问题：（1）若测得（如图1），求的值；（2）对同一条抛物线，孔明将三角板绕点旋转到如图2所示位置时，过作轴于点，测得，写出此时点的坐标，并求点的横坐标；（3）对该抛物线，孔明将三角板绕点旋转任意角度时惊奇地发现，交点、的连线段总经过一个固定的点，试说明理由并求出该点的坐标图2图111Winger Tuivasa-Sheck, who scored two tries in the Kiwis 20-18 semi-final win over England, has been passed fit after a lower-leg injury, while Slater has been named at full-back but is still recovering from a knee injury aggravated against USA.Both sides boast 100% records heading into the encounter but Australia have not conceded a try since Josh Charnleys effort in their first pool match against England on the opening day.Aussie winger Jarryd Hayne is the competitions top try scorer with nine, closely followed by Tuivasa-Sheck with eight.But it is recently named Rugby League International Federation player of the year Sonny Bill Williams who has attracted the most interest in the tournament so far.The Kiwi - with a tournament high 17 offloads - has the chance of becoming the first player to win the World Cup in both rugby league and rugby union after triumphing with the All Blacks in 2011."Id give every award back in a heartbeat just to get across the line this weekend," said Williams.The (lack of) air up there Watch mCayman Islands-based Webb, the head of Fifas anti-racism taskforce, is in London for the Football Associations 150th anniversary celebrations and will attend Citys Premier League match at Chelsea on Sunday."I am going to be at the match tomorrow and I have asked to meet Yaya Toure," he told BBC Sport."For me its about how he felt and I would like to speak to him first to find out what his experience was."Uefa hasopened disciplinary proceedings against CSKAfor the "racist behaviour of their fans" duringCitys 2-1 win.Michel Platini, president of European footballs governing body, has also ordered an immediate investigation into the referees actions.CSKA said they were "surprised and disappointed" by Toures complaint. In a statement the Russian side added: "We found no racist insults from fans of CSKA." Baumgartner the disappointing news: Mission aborted.The supersonic descent could happen as early as Sunda.The weather plays an important role in this mission. Starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. The balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to-day weather lives. It will climb higher than the tip of Mount Everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. As he crosses the boundary layer (called the tropopause),e can expect a lot of turbulence.The balloon will slowly drift to the edge of space at 120,000 feet ( Then, I would assume, he will slowly step out onto something resembling an Olympic diving platform.They blew it in 2008 when they got caught cold in the final and they will not make the same mistake against the Kiwis in Manchester.Five years ago they cruised through to the final and so far history has repeated itself here - the last try they conceded was scored by Englands Josh Charnley in the opening game of the tournament.That could be classed as a weakness, a team under-cooked - but I have been impressed by the Kangaroos focus in their games since then.They have been concentrating on the sort of stuff that wins you tough, even contests - strong defence, especially on their own goal-line, completing sets and a good kick-chase. Theyve been great at all the unglamorous stuff that often goes unnoticed in the stands but not by your team-mates.It is as though their entire tournament has been preparation for the final.In Johnathan Thurston, Cooper Cronk, Cameron Smith and either Billy Slater or Greg Inglis at full-back they have a spine that is unmatched in rugby league. They have played in so many high-pressure games - a priceless asset going into Saturday.The Kiwis are a lot less experienced but winning a dramatic match like their semi-final against England will do wonders for their confidence.They defeated Australia in the Four Nations final in 2010 and the last World Cup, and know they can rise to the big occasion.第 6 页 共 6 页