bđt tam giác:
\(\hept{\begin{cases}a+b>c\Leftrightarrow ac+bc>c^2\\b+c>a\Leftrightarrow ab+ac>a^2\\a+c>b\Leftrightarrow ab+bc>b^2\end{cases}}\)
Cộng theo vế: \(2\left(ab+bc+ac\right)>a^2+b^2+c^2\)
cho tam giac ABC can tai A . M la mot diem thay doi tren BC . c/m rang khi M la mot diem bat ki tren BC thi tong khoang canh tu M den 2 canh AB va AC la ko doi
cho tam giac nhon ABC ve ra phia ngoai tam giac vuong can ABD va AEC(vuong can tai B va tai C ). tren tia doi cua tia AH lay diem I sao cho AI=BC(AH vuong goc voiBC(H thuoc BC)cm
a)tam giac ABI=tam giac BDC
b)Bivuong goc voi CD
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.
1.a) \(\frac{3}{4}\)x -- \(\frac{1}{3}\)= \(\frac{2}{3}\)x -- \(\frac{3}{5}\)
b) \(\frac{\left(-5\right)^{32}.20^{43}}{\left(-8\right)^{29}.125^{25}}\)
c) \(\left(\frac{1}{2}-x\right)^2\)= \(\left(-2\right)^2\)
2. Tim do dai 2 canh cua 1 hinh chu nhat ,biet ti so giua cac canh cua no bang 0,6 va chu vi bang 32cm .
3. Cho a = \(^{8^{12}.25^{19}}\). Tim so chu so cua a .
4. Cho tam giac ABC vuong tai A . Tia phan giac cua goc B cat canh AC tai D
a) Cho biet \(\widehat{ABC}\)= 400 . Tinh so do goc ABD
b) Tren canh BC lay diem E sao cho BE = BA . Chung minh tam giac BAD = tam giac BED va DE _|_ BC
c) Goi F la giao diem cua BA va ED . Chung minh rang tam giac ABC = tam giac EBF
d) Ve CK vuong goc voi BD tai K . Chung minh rang ba diem K , F , C thang hang .
neu a,b,c la 3 canh cua mot tam giac thoa man a^2+b^2>5c^2 thi c la canh nho nhat
cho tam giac abc vuog tai a (ab<ac). tren canh bc lay diem h sao cho ba=bh.qua h ke duong thag vuong goc vs bc va cat ac,ba lan luot tai e,f
a. cm ea=eh
b. cm 2 tam giác aef=hec
c. cm tam giac efc la tam giac can tai e
d.cho i la trung diem cua fc,cm b,e,i thang hang
cho tam giac ABC co goc A = 90 do va BC = 2 * AB ; E la trung diem cua BC . tia phan giac cua goc B cat canh AC o D
A ) chung minh DB la phan giac cua goc ADE
B ) chung minh BD = DC
C) tinh goc B , goc C cua tam giac ABC
cho tam giac can ABC( AB=AC), tren cac canh AB va AC lay tuong ung 2 diem D va E sao cho AD=AE. Goi M la trung diem cua BC.Cmr:
a)DE//BC
b)tam giac MBD=tam giac MCE
c)tam giac AMD=tam giac AME
cho tam giac ABC can tai A.Goi D la trung diem cua canh BC.Ke DE vuong AB,DE vuong AC, CMR: a) tam giac DEB = tam giac DFC b) tam giac AED = tam giac AFD c) AD la tia phan giac cua BAC
CHO TAM GIÁC ABC CAN TAI A GOI D LA TRUNG ĐIỂM CANH BC KẺ DE VUONG GOC AB, DE VUONG GOC AC
CMR: TAM GIAC DEB=TAM GIAC DFC
b) tam giac AED=TAM GIAC AFD
C) AD LA TIA PHAN GIAC CUA GOA BAC
