cho tam giac ABC nhon co goc A = 60 do va hai duong phan giac BD va CE cat nhau o I tinh so do goc BIC b) IF la phan giac cua tam giac IBC chung minh tam giác IBE= tam giac BIF va tam giác CID = tam guac CIF
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Bai 1 cho goc XOY90 do,lay A,B thuc Ox(A nam giua O va B)lay C,D thuoc Oy sao cho OAOC,ABCD
1)Tam giac OBD can
2)So sanh AD ba BC
3)Goi I la giao diem AD va BC tam gia IBDva tam giacIAC la cac tam giac gi
4)Chung minh tamgiaOACtam giacOCI
Bai 2 Cho tam giac ABC can tai A lay diem D thuo AB.tren tia doi cua tia CA lay CEBD,DE cat BC o M
Chung minh M la trung diem DE
Bai 4Cho tam giac ABC nhon co goc A60 do,hai duong phan giac BD va CF cat nhau tai I
1)Tinh goc BIC
2)IF la duong phan g...
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Bai 1 cho goc XOY<90 do,lay A,B thuc Ox(A nam giua O va B)lay C,D thuoc Oy sao cho OA=OC,AB=CD
1)Tam giac OBD can
2)So sanh AD ba BC
3)Goi I la giao diem AD va BC tam gia IBDva tam giacIAC la cac tam giac gi
4)Chung minh tamgiaOAC=tam giacOCI
Bai 2 Cho tam giac ABC can tai A lay diem D thuo AB.tren tia doi cua tia CA lay CE=BD,DE cat BC o M
Chung minh M la trung diem DE
Bai 4Cho tam giac ABC nhon co goc A=60 do,hai duong phan giac BD va CF cat nhau tai I
1)Tinh goc BIC
2)IF la duong phan giac cua tam giac IBC
3)Chung minh+)tam giac BID=tam giac BIF
+)tam giac CID=tam giac CIF
ai biet lam bai nay thi giup minh nhanh len nhe minh dang can gap
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Bai 1Cho tam giac ABC can o A tren tia doi AC lay ADAC1) tam giac ABD la tam giac gi 2) chung minh goc DBCgo BDC+go DCB3) tinh goc DBCBai 2 Cho goc xOy90 do,lay A,B thuo Ox(A nam giua O va B),lay C,D thuoc Oy sao cho OAOC,ABCD1) Chung minh tam giac OBD an2) So sanh AD va BC3) Goi I la giao diem AD va BC tam giac IBD va tam giac IAC la cac tam giac gi4)cm tam giac OAItam giac OCIBai 3 cho tam giac ABC can tai A ,lay diem D thuoc AB.Trn tia doi cua tia CA lay CEBD,DE cat BC o M1)Chung minh M la tr...
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Bai 1Cho tam giac ABC can o A tren tia doi AC lay AD=AC
1) tam giac ABD la tam giac gi
2) chung minh goc DBC=go BDC+go DCB
3) tinh goc DBC
Bai 2 Cho goc xOy<90 do,lay A,B thuo Ox(A nam giua O va B),lay C,D thuoc Oy sao cho OA=OC,AB=CD
1) Chung minh tam giac OBD an
2) So sanh AD va BC
3) Goi I la giao diem AD va BC tam giac IBD va tam giac IAC la cac tam giac gi
4)cm tam giac OAI=tam giac OCI
Bai 3 cho tam giac ABC can tai A ,lay diem D thuoc AB.Trn tia doi cua tia CA lay CE=BD,DE cat BC o M
1)Chung minh M la trung diem DE
Bai 4 cho tam giac ABC nhon o A =60 do ,hai duong phan giac BD va CE cat nhau tai Ii
1)Tinh BIC
2)IE la duong phan giac cua tam giac IBC
Chung minh+)tam giac BIE=tam giac BIF
+)tam giac CID=tam giac CIF
1.a) \(\Delta ABC\)cân tại A\(\Rightarrow AB=AC\).Mà \(AD=AC\Rightarrow AB=AD\)
Xét \(\Delta ABD\)có \(AB=AD\Rightarrow\Delta ABD\)cân tại A
b)Có \(\widehat{ABC}=\widehat{ACB}\left(1\right)\)( do \(\Delta ABC\)cân)
\(\widehat{ABD}=\widehat{ADB}\left(2\right)\)( do \(\Delta ABD\)cân )
Từ \(\left(1\right);\left(2\right)\Rightarrow\widehat{ABC}+\widehat{ABD}=\widehat{ACB}+\widehat{ADB}\)
\(\Rightarrow\widehat{DBC}=\widehat{ACB}+\widehat{ADB}\)hay \(\widehat{DBC}=\widehat{DCB}+\widehat{BDC}\left(dpcm\right)\)
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2.
a)Nối A vs C
có\(OA=0C;AB=CD\Rightarrow OA+AB=OC+CD\)
hay \(OB=OD\).Xét \(\Delta OBD\)có \(OB=OD\Rightarrow\Delta OBD\)cân tại O
b) Xét \(\Delta OAD\)và \(\Delta OCB\)có:
\(OA=OB\left(gt\right)\)
\(\widehat{AOB}:chung\)
\(OB=OD\left(cmt\right)\)
\(\Rightarrow\Delta OAD=\Delta OCB\left(c.g.c\right)\Rightarrow AD=CB\left(dpcm\right)\)
c)Có \(\Delta OAD=\Delta OCB\Rightarrow\widehat{ADO}=\widehat{CBO}\)
Xét \(\Delta ACD\)và \(\Delta CBA\)có: \(AD=CD\)
\(\widehat{ADO}=\widehat{CBO}\)
\(CD=BA\)
\(\Rightarrow\Delta ACD=\Delta CBA\left(c.g.c\right)\Rightarrow\widehat{CAD}=\widehat{BCA}\Rightarrow\Delta IAC\)cân tại I
Làm tương tự bạn => tam giác IBD cân tại I ( tam giác ADB = tam giác CBD => Góc ADB= góc CBD)
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Câu c bài 1:
có\(\widehat{ABC}=\frac{180^o-\widehat{BAC}}{2}\)và\(\widehat{ABD}=\frac{180^o-\widehat{DAB}}{2}\)
\(\Rightarrow\widehat{ABC}+\widehat{ABD}=\frac{180^o-\widehat{BAC}}{2}+\frac{180^o-\widehat{DAB}}{2}\)
\(\Leftrightarrow\widehat{DBC}=\frac{180^o+180^o-\left(\widehat{BAC}+\widehat{DAB}\right)}{2}\)
\(\Leftrightarrow\widehat{DBC}=\frac{360^o-\widehat{DAC}}{2}=\frac{360^o-180^o}{2}=\frac{180^o}{2}=90^o\)
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cho tam giac ABC co goc A = 64 do hai tia phan giac cua goc B va goc C cat nhau tai I
a+ tinh goc BIC
b) ke duong phan giac qua I song song voi BC cat AB tai M va AC tai N chung minh rang tam giac BMI va tam giac CNI can
c) chung minh MN=BN+CN
Cho tam giac ABC, goc A =60 do. Tia phan giac cua goc Bva C cat cac canh doi dien tai D va E, BD va CE cat nhau tai O. Tia phan giac cua goc BOC cat BC tai F. Chung minh a, OD=OE=OF b, Tam giac DEF la tam giac deu.
Cho tam giac ABC co goc A bang 120 do. Hai duong phan giac BD va CE cat nhau tai I.
a, Tinh so do goc BIC
b, Noi Ai keo dai cat BC tai F. Chung minh DE vuong goc voi FE.
hai tia phan giac trong tai dinh B va C cua tam giac ABC cat nhau tai O niet BOC bang 130 do
a) tinh so do goc A
b) hai tia phan giac ngoai tai dinh B va C cua tam giac ABC cat nhau tai P chung minh A.O,P thang hang
c) tam giac ABC la tam giac gi de OP la phan giac goc BOC
cau 1 cho tam giac can abc co ab=ac=17 va bc=30 ve ra ngoai tam giac abc tam giac bcd voi cbd=90 do va cd song song voi ab tinh do dai bd
cau 2 cho tam giac abc co goc b =70 do goc c =40 do cac duong cao bd va ce cat nhau tai h goi i la trung diem cua ah m la giao cua tia phan giac goc eid voi bc tinh goc imd
cho tam giac abc nhon noi tiep (O;R) co ab>ac tia phan giac cua goc a cat bc tai i va cat (O) tai d. ha be va cf vuong goc voi ad tai e va f, ve duong cao ah cua tam giac abc
c, ve im vuong goc ab tai m chung minh f,m,h thang hang
d, bf cat ce tai k chung minh ak la phan giac ngoai tam giac abc
cho tam giac abc co goc a bang 90 do. bd la phan giac cua goc b ve de vuong goc bc .goi f la giao diem cua ab va de
a, chung mijh tam giac abd = tam giac ebd va duong trung truc cua ae
b, chung minh tam giac dcf can
c, khi tam giac abc co goc b bang 60 do , c = 30 do va bc = 12 cm . tinh do dai dc