组卷网>知识点选题>化角为边法判断三角形形状
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1 . 在eqId64b9b599fdb6481e9f8d9a94c102300b中,角eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5ceqId19a4eb16029e4550a14f2afe4741a3c3所对的边分别为eqId70a27b6ddf6b478285353abb3b1f3741eqIdaea992e70d4943e49e893817eb885ed7eqId44925af6fb19413689ba5616e3647cba.则下列命题正确的是(   )
A.若eqId856c4a8cc93d41ea85e48501d3c5e6d8eqId7fa00d9e89d144858b58ced60919b1b3eqIdce73b6015f984ae3a8137b54067a2775,则eqId2e37cf7454184861989b8989980a7e9f
B.若eqId9db00393d5ef4a1697f88b3448952ccc,则eqId30c12283e46b4115bb4475066d23eff0
C.若eqId71f9e7c62be54787baf69dda1f1ffd7f,则eqId64b9b599fdb6481e9f8d9a94c102300b为钝角三角形
D.若eqIdd7a2aa5f022b4892bd87af662f713413eqId7fa00d9e89d144858b58ced60919b1b3eqIdb9a9b49f7375459d80ee469ede3bcba2eqId64b9b599fdb6481e9f8d9a94c102300b的面积为3
2 . 在eqIdb1803dcd0646465285ffbf361c487652中,内角eqId10bbe48f886a4fa78fdf8c1fd064f9b4所对的边分别为eqId0ce93bfa1f6a4a23b3258410dd19847a,下列条件中能说明eqId64b9b599fdb6481e9f8d9a94c102300b为直角三角形的条件有_________(写出所有符合条件的序号)
eqId48277a14aeb2420bba0f93a84c0d3aea;   
② eqIdf671196577a34f40a698cf441f98dcbf
eqId7432deb6f5ef4a08baadae00ee4267b7;               
④ eqId7ccc581b5f3d4a229c65750c0e6d0793.
3 . eqId0ce93bfa1f6a4a23b3258410dd19847a分别为eqId7d9a9f629a9249f9b27148eed1fce4a5中三个内角eqId10bbe48f886a4fa78fdf8c1fd064f9b4的对边,下列结论中正确的是(   )
A.若eqIda1431f21126045c79b0e73b5824aef56,则eqId64b9b599fdb6481e9f8d9a94c102300b为等腰三角形.
B.若eqId9db00393d5ef4a1697f88b3448952ccc,则eqId30c12283e46b4115bb4475066d23eff0
C.若eqId0ad1f0b364f044feab7423c5a4ebe0b2,则符合条件的eqId64b9b599fdb6481e9f8d9a94c102300b有且仅有两个.
D.若eqId5470035d1287496094c77f2878fef1ca,则eqId64b9b599fdb6481e9f8d9a94c102300b为钝角三角形.
4 . 已知△ABC的角ABC所对的边分别是abc,设向量eqId4b3ec5d571d24dd9bc22e8dbdcd941ab.
(1)若eqId7ddf6f8a43f549e89aa00bbd3f706cb5,求证:eqId64b9b599fdb6481e9f8d9a94c102300b为等腰三角形;
(2)若eqId72101b2122284a1da8d37d9a4313a3d1,边长eqIdf33085e1bdfc4c56904f2a8a10432355eqId7626d02402f84ba1a6e4f6ff93710d39,求eqId64b9b599fdb6481e9f8d9a94c102300b的面积.
5 . 在eqId64b9b599fdb6481e9f8d9a94c102300b中,若eqIdfbb26003c68d4e6ea899a1e09eddbb31,则eqId64b9b599fdb6481e9f8d9a94c102300b的形状为(   ).
A.等边三角形B.等腰三角形
C.等腰直角三角形D.等腰或直角三角形
6 . 在eqId64b9b599fdb6481e9f8d9a94c102300b中,内角ABC的对边分别为abc,已知eqId15a1cdab3e7e4ed687b51373fdc59589,则eqId64b9b599fdb6481e9f8d9a94c102300b是(   )
A.等腰三角形B.直角三角形C.等腰直角三角形D.等腰或直角三角形
7 . 已知△ABC的内角ABC所对的边分别为abc,下列四个命题中正确的是(   )
A.若eqId843e060c8a784abeb1f6ee3910b084fa,则B只有一解
B.若eqId1fbf61e933314caf812479a05276dd06,则△ABC一定是锐角三角形
C.若bcosCccosBb,则△ABC一定是等腰三角形
D.若acosAbcosB,则△ABC一定是等腰三角形
8 . 已知eqId64b9b599fdb6481e9f8d9a94c102300b的三条边eqId0ce93bfa1f6a4a23b3258410dd19847a和与之对应的三个角eqId10bbe48f886a4fa78fdf8c1fd064f9b4满足等式eqId6081af32bfa0467193d69b187f2529a2则此三角形的形状是(   )
A.等腰三角形B.直角三角形
C.等腰或直角三角形D.等腰直角三角形
解答题 | 一般(0.65) | 2021·湖南高一月考
9 . 在eqId64b9b599fdb6481e9f8d9a94c102300b中,角ABC的对边分别为eqId485b8849810342b191e40d31b530da19
(1)若eqId2234a575c5504660b2d4922640ee83a1,求eqIdc1d1d0a1c54e4ccc9308e8a97b4c4e0a的值;
(2)若eqIdb280b71005d64be0b93506e61c4852de,判断eqId64b9b599fdb6481e9f8d9a94c102300b的形状.
10 . 在eqId64b9b599fdb6481e9f8d9a94c102300b中,角eqId32e6b3a6aabd463cbd301d104e9c2aad所对应的边分别为eqIdc9b6648789574cbab558be8c948cfe27.
(1)若eqIda61ecee065f241f0a80ce386d175cf8d,求eqId052844cae8574a8ab842c38a039baac0的值;
(2)若eqId675aaabd6e29452095f8c1b7c37bd66ceqId9a53e01b36a34526a1c2bdc20e9871b2,试判断eqId64b9b599fdb6481e9f8d9a94c102300b的形状.
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