配套习题- “三点定型法”证明线段等积式（比例式）策略 -【青果学院】

挑战习题

1/5单选题

难度：

如图，P是△ABC的边AC上一点，连接BP，以下条件中不能判定△ABP∽△ACB的是

（　　）

A
B
C	∠ABP=∠C
D	∠APB=∠ABC

提示1：: PHA+5Lik57uE5a+55bqU6L6555qE5q+U55u4562J77yM5LiU55u45bqU55qE5aS56KeS55u4562J77yM5q2k5pe25Lik5Liq5LiJ6KeS5b2i55u45Ly877yM5omA5LulQumUmeivrzwvcD4=

正确答案：Qg==

PGRpdj7op6PvvJpB5q2j56Gu77yM56ym5ZCI5Lik57uE5a+55bqU6L6555qE5q+U55u4562J5LiU55u45bqU55qE5aS56KeS55u4562J55qE5Lik5Liq5LiJ6KeS5b2i55u45Ly877ybPGJyPkLkuI3mraPnoa7vvIzkuI3nrKblkIjkuKTnu4Tlr7nlupTovrnnmoTmr5Tnm7jnrYnkuJTnm7jlupTnmoTlpLnop5Lnm7jnrYnnmoTkuKTkuKrkuInop5LlvaLnm7jkvLzvvJs8YnI+Q+ato+ehru+8jOespuWQiOacieS4pOe7hOinkuWvueW6lOebuOetieeahOS4pOS4quS4ieinkuW9ouebuOS8vO+8mzxicj5E5q2j56Gu77yM56ym5ZCI5pyJ5Lik57uE6KeS5a+55bqU55u4562J55qE5Lik5Liq5LiJ6KeS5b2i55u45Ly8Ljxicj7mlYXpgIlCLjwvZGl2Pg==

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2/5单选题

难度：

如图，在正三角形ABC中，D，E分别在AC，AB上，且，AE=BE，则有

（　　）

A	△AED∽△ABC
B	△AED∽△CBD
C	△AED∽△ABD
D	△AED∽△BED

提示1：: PHA+5qC55o2u5Lik6L655a+55bqU5oiQ5q+U5L6L5LiU5aS56KeS55u4562J55qE5Lik5Liq5LiJ6KeS5b2i55u45Ly877yM5Y+v5Yik5a6a4pazQUVE4oi94pazQ0JELjwvcD4=

正确答案：Qg==

PGRpdj7op6PvvJriiLVBRO+8mkFDPTHvvJoz77yMPGJyPuKItEFE77yaREM9Me+8mjLvvJs8YnI+4oi14pazQUJD5piv5q2j5LiJ6KeS5b2i77yMPGJyPuKItEFCPUJDPUFD77ybPGJyPuKItUFFPUJF77yMPGJyPuKItEFF77yaQkM9QUXvvJpBQj0x77yaMjxicj7iiLRBRO+8mkRDPUFF77yaQkPvvJs8YnI+4oi14oigQeS4uuWFrOWFseinku+8jDxicj7iiLTilrNBRUTiiL3ilrNDQkTvvJs8YnI+5pWF6YCJQi48L2Rpdj4=

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3/5单选题

难度：

如图，△ABC中，P为AB上一点，在下列四个条件中：
①∠ACP=∠B；②∠APC=∠ACB；③AC²=AP•AB；④AB•CP=AP•CB，能满足△APC与△ACB相似的条件是（　　）

A	①②③
B	①③④
C	②③④
D	①②④

提示1：: PHA+5qC55o2u55u45Ly85LiJ6KeS5b2i55qE5Yik5a6a5pa55rOV5a+55ZCE5Liq5p2h5Lu26L+b6KGM5YiG5p6Q77yM5LuO6ICM5b6X5Yiw5pyA5ZCO562U5qGILjwvcD4=

正确答案：QQ==

PGRpdj7op6PvvJriiLXiiKBBPeKIoEE8YnI+4oi04pGg4oigQUNQPeKIoELvvIzikaHiiKBBUEM94oigQUNC5pe26YO955u45Ly877ybPGJyPuKItUFDPHN1cD4yPC9zdXA+PUFQ4oCiQUI8YnI+4oi0QUPvvJpBQj1BUO+8mkFDPGJyPuKItOKRouebuOS8vO+8mzxicj7ikaPmraTkuKTkuKrlr7nlupTovrnnmoTlpLnop5LkuI3mmK/iiKBB77yM5omA5Lul5LiN55u45Ly8Ljxicj7miYDku6Xog73mu6HotrPilrNBUEPkuI7ilrNBQ0Lnm7jkvLznmoTmnaHku7bmmK/ikaDikaHikaIuPGJyPuaVhemAiUEuPC9kaXY+

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4/5单选题

难度：

点P为矩形ABCD内部或边上的点，若AB＞2BC，那么使△PAD∽△PDC的点P的个数有（　　）

A	1个
B	2个
C	3个
D	4个

提示1：: PHA+5YWo562J5piv54m55q6K55qE55u45Ly877yM5omA5Lul54K5UOS4jueCuULph43lkIjnrKblkIjopoHmsYLvvJs8L3A+

提示2：: PHA+5Zug5Li6QULvvJ4yQkPvvIzmiYDku6Xku6VDROeahOS4uuebtOW+hOS9nOWchuS6pEFC5LqO54K5UOS4jlDigLLvvIzmoLnmja7nm7TlvoTmiYDlr7nnmoTlnIblkajop5LmmK/nm7Top5LljbPlj6/or4HlvpfvvJs8L3A+PHA+PGltZyBzdHlsZT0id2lkdGg6IDE0OXB4OyBoZWlnaHQ6IDEwNXB4OyIgYWx0PSIiIGRhdGEtY2tlLXNhdmVkLXNyYz0iaHR0cHM6Ly9wMi5xaW5nZ3VvLmNvbS9HMS9NMDAvMDYvQTcvckJBQ0ZGTVFZbGpqZGtLZkFBQVVuUmFPd0djODIyLnBuZyIgc3JjPSJodHRwczovL3AyLnFpbmdndW8uY29tL0cxL00wMC8wNi9BNy9yQkFDRkZNUVlsampka0tmQUFBVW5SYU93R2M4MjIucG5nIj48L3A+

提示3：: PHA+5Zyo55+p5b2i5YaF6YOo5Lmf5pyJ5LiA54K577yMRFDiiqVBQ+WNs+WPry48L3A+PHA+PGltZyBzdHlsZT0id2lkdGg6IDE2OHB4OyBoZWlnaHQ6IDcwcHg7IiBhbHQ9IiIgZGF0YS1ja2Utc2F2ZWQtc3JjPSJodHRwczovL3AyLnFpbmdndW8uY29tL0cxL00wMC8wNi9BNy9yQkFDRkZNUVlsaURPWXBpQUFBSzRFYVRDRVU2NTcucG5nIiBzcmM9Imh0dHBzOi8vcDIucWluZ2d1by5jb20vRzEvTTAwLzA2L0E3L3JCQUNGRk1RWWxpRE9ZcGlBQUFLNEVhVENFVTY1Ny5wbmciPjwvcD4=

正确答案：RA==

PHA+PGltZyBzdHlsZT0id2lkdGg6IDMxMHB4OyBoZWlnaHQ6IDQ4NHB4OyIgYWx0PSIiIGRhdGEtY2tlLXNhdmVkLXNyYz0iaHR0cHM6Ly9wMi5xaW5nZ3VvLmNvbS9HMS9NMDAvMzgvREIvckJBQ0UxTVdseml6LUJxeEFBQTI0amRyTThvOTMwLnBuZyIgc3JjPSJodHRwczovL3AyLnFpbmdndW8uY29tL0cxL00wMC8zOC9EQi9yQkFDRTFNV2x6aXotQnF4QUFBMjRqZHJNOG85MzAucG5nIj7igIs8L3A+PHA+4oi14oigQ0RQK+KIoEFEUD05MMKw77yMPGJyPuKItOKIoEFEUD3iiKBEQ1DvvIw8YnI+4oi04pazUEFE4oi94pazUERD77yOPGJyPuKItOWFseaciTTkuKrvvI48YnI+5pWF6YCJRO+8jjwvcD4=

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5/5单选题

难度：

5.如图，在△ABC中，∠BAC=90°，AD⊥BC，垂足为点D，∠ABC的平分线分别交AD、AC于点E、F，连接DF，下列结论中错误的是（　　）

A	△ABD∽△CAD
B	△BDF∽△DFA
C	△BDE∽△BAF
D	△ABE∽△CBF

提示1：: IOeUseKIoEJBQz05MMKw77yMQUTiiqVCQ++8jOW+l+WIsOKIoEJBRD3iiKBD77yM4oigREFDPeKIoEFCRO+8jOagueaNruacieS4pOe7hOWvueW6lOinkuebuOetieeahOS4pOS4ieinkuW9ouebuOS8vOW+l1J04pazQUJE4oi9UnTilrNDQUQ=

提示2：: IOWPiOKIoEFCRj3iiKBDQkbvvIzlho3moLnmja7mnInkuKTnu4Tlr7nlupTop5Lnm7jnrYnnmoTkuKTkuInop5LlvaLnm7jkvLzmmJPlvpdSdOKWs0JEReKIvVJ04pazQkFG77yM4pazQUJF4oi94pazQ0JG77yb

提示3：: IOiAjOimgeKWs0JERuKIveKWs0RGQe+8jOmcgOa7oei2s0RG5Li655u06KeS5LiJ6KeS5b2iQURD5pac6L655LiK55qE5Lit57q/77yM5qC55o2u6aKY5oSP5LiN6IO95b6X5Yiw6L+Z5Liq57uT6K66Lg==

正确答案：Qg==

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