cho tam giac ABC can tai A co canh day bang 14 cm, ke Ad la tia phan giac cua goc BAC( D thuoc BC). tinh do dai canh AB biet AD= 15cm
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cho tam giac ABC can tai A co canh day bang 14 cm, ke Ad la tia phan giac cua goc BAC( D thuoc BC). tinh do dai canh AB biet AD= 15cm
Xét \(\Delta ABC\)cân tại \(A\left(gt\right):\)
\(\Rightarrow AB=AC\)
Xét \(\Delta ABD\)và \(\Delta ACD,:\)
\(\widehat{BAD}=\widehat{CAD}\left(AD:tpg\widehat{BAC}\right)\)
\(AB=AC\left(cmt\right)\)
\(AD\)chung
\(\Leftrightarrow\Delta ABD=\Delta ACD\left(c.g.c\right)\)
\(+,\Rightarrow BD=CD\)( 2 cạnh t/ứ)
\(\Rightarrow D\)là trung điểm của \(BC\)
\(\Rightarrow BD=CD=\frac{BC}{2}=\frac{14}{2}=7\left(cm\right)\)
\(+,\Rightarrow\widehat{BDA}=\widehat{CDA}\)( 2 góc t/ứ)
Mà \(\widehat{BDA}+\widehat{CDA}=180^0\)
\(\Rightarrow2\widehat{BDA}=180^0\Leftrightarrow\widehat{BDA}=90^0\)
\(\Rightarrow\Delta ABD\perp\)tại \(D\)
\(\Rightarrow AD^2+BD^2=AB^2\left(Py-ta-go\right)\)
\(\Rightarrow15^2+7^2=AB^2\)
\(\Rightarrow AB^2=225+49\)
\(\Rightarrow AB^2=274\)
\(\Rightarrow AB=\sqrt{274}cm\)
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1. cho tam giac ABC can tai A, ve diem M, Nbat ki tren duong trung truc ca doan thang BC.CM:a,tam giac MBCcan tai Mb, MNCMNB2.cho tam giac ABC cao M la trung diem cua canh BC. qua B ke duong thang Bx AC, qua C ke Cy AB. giao diem cua Cy, Bx la D. CM: A, D, M thang hang.3. do dai 2 canh goc vuong cua mot tam giac vuong ti le voi 7 va 24. chu vi tam giac bang 112. tinh do dai canh huyen.4.cho tam giac ABC can tai A, canh day nho hon canh ben. duong trung truc cua AC cat BC tai M. tren tia doi cu...
Đọc tiếp
1. cho tam giac ABC can tai A, ve diem M, Nbat ki tren duong trung truc ca doan thang BC.CM:
a,tam giac MBCcan tai M
b, MNC=MNB
2.cho tam giac ABC cao M la trung diem cua canh BC. qua B ke duong thang Bx \\ AC, qua C ke Cy \\ AB. giao diem cua Cy, Bx la D. CM: A, D, M thang hang.
3. do dai 2 canh goc vuong cua mot tam giac vuong ti le voi 7 va 24. chu vi tam giac bang 112. tinh do dai canh huyen.
4.cho tam giac ABC can tai A, canh day nho hon canh ben. duong trung truc cua AC cat BC tai M. tren tia doi cua AM lay N \ AN = BM.
a, CM: 2 goc AMC va BAC bang nhau
b, CM: CM = CN
c, de CM vuong voi CN hi tam giac ABC phai co them dieu kien gi?
5. cho tam giac ABC deu. tren tia doi cua tia phan giac goc BAC lay D \ AD = AB. tinh cac goc cua tam giac DBC.
Cho tam giac ABC can tai A ke AH vung goc voi BC (H thuoc BC )
a, Chung minh AH la tia phan giac cua goc BAC
b, Ke HD vuong goc voi AB ( D thuoc AB) , HE vuong goc voi AC ( E thuoc AC). Chung minh tam giac HDE can
c, Neu cho AB = 29 cm , AH = 20 cm .Tinh do dai BC
d,Chung minh BC//DE
e, Neu cho goc BAC =120 do thi tam giac HDE tro thanh tam giac gi ? Vi sao
cho tam giac abc co canh ab bang 62 cm. Neu keo dai canh bc mot doan cd dai bang 30cm thi ta co tam giac abd la tam giac can voi ab bang ad ca tam giac acd co chieu cao ke tu c bang 18cm. biet chu vi cua tam giac abd bang 206cm.
a) tinh dien tich tam giac acd.
b)tinh dien tich tam giac abc
CHO TAM GIAC ABC CO AD LA PHAN GIAC CUA GOC A (D THUOC BC). KE DEVUONG GOC VOI AB, KE DF VUONG GOC VOI AC
a, CHUNG MINH TAM GIAC AED= TAM GIAC AFD
b, TIA FD CAT TIA AB TAI P, TIA ED CAT TIA AC TAI Q. CHUNG MINH AP=AQ
c, TIA AD CAT PQ TAI M. CHUNG MINH AM LA DUONG TRUNG TRUC CUA DOAN THANG PQ
d, CHO GOC BAC=50 DO. TINH SO DO GOC APQ VA GOC AQP
Cho tam giac abc tia phan giac cua goc abc cat canh ac tai d tu d ke duong thang //bc dg thanh nay cat canh ab tai diem e tia phan giac cua goc aed cat ad tai f ctr a,tam giac ebdco 2 goc bang nhau b,ef//bd
Trong hinh 73 , tam giac ABC co goc A bang 62 do ; CD , BD lan luot la duong phan giac voi cac goc ACB va CDB
a) Tinh so do cua goc CDB
b) Ke tia AD , tinh so do cua goc CAD
c) Diem D co cach deu ba canh cua tam giac ABC khong ? Tai sao ?
Bai 1;Cho tu giac ABCD (AB//CD) co cac tia phan giac cua cac goc C va D gap nhau tai I thuoc canh ben BC
CMR;AD bang tong cua hai day
Bai 2;cho tam giac ABC vuong tai A,BC=2cm.Ve tam giac ACE vuong tai E (E khac phia doi voi AC ).
CMR;AECB la hinh thang vuong.Tinh cac goc va cac canh cua no
Cho tam giac ABC can tai A co AD la duong trung tuyen
a)Chung minh tam giac ABD= tam gaic ACD va AD vuong goc voi BC
b)Cho AB=10cm,BC=16cm. Tinh do dai AD va so sanh cac goc cua tam giac ABC.
c) Ve duong trung tuyen CF cua tam giac ABC cat AD tai M. Tinh do dai AM.
d) Ve DH vuong goc AC tai H, tren canh AC va canh DC lan luot lay hai diem E,K sao cho AE=AD va DK=DH. Chung minh: EK vuong goc voi BC
A,
xét \(\Delta ABD\)và \(\Delta ACD\)
CÓ \(\hept{\begin{cases}AB=AC\\chungAD\\BD=DC\end{cases}}\)
SUY RA \(\Delta ABD\)=\(\Delta ACD\) (C.C.C) (1)
=> \(\widehat{BDA}\)=\(\widehat{CDA}\)
MÀ \(\widehat{BDA}\)+\(\widehat{CDA}\)=180
=> \(\widehat{BDA}\)=\(\widehat{CDA}\)=90
B, (1) => BC=DC=1/2 BC=8
ÁP DỤNG ĐỊNH LÍ PITAGO TA CÓ
\(AB^2=AD^2+BD^2\)
=> AD^2=36
=>AD=6
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