Cho tam giac ABC vuong tai A , AB=AC . Qua A ve duong thang d sao cho B va C nam cung phia doi voi duong thang d . Ke BH va CK vuong goc voi d . Chung minh :
a, AH=CK
b, HK=BH+ CK
cho tam giac ABC vuong tai A, M la trung diem cua AC. qua A ve duong thang d sao cho B va C nam cung phia doi voi duong thang d. ke BH va CK vuong goc voi d. chung minh a)AH=CK b) HK=BH+CK
cho tam giac abc vuong o A,ab=ac .qua a ve dg thang d sao cho B va C nam cung phia doi voi dg thang d ,ke BH va KC vuong goc voi d chung minh
a,ah=ck
b, hk=bh+ck
giupminh voi sap thi rui
Cho tam giac abc vuong tai a, ab=ac. Qua a ke duong thang d sao cho b va c nam cung phia doi voi d. Ke bd va ce vuong goc voi d d,e thuoc d. Chung minh bd=ae
cho tam giac abc vuong can tai a. mot duong thang d bat ki luon di qua a. ke bh va ck vuong goc voi duong thang d. cmr tong bh^2 + ck^2 co gia tri khong doi
Giải:
Ta có: \(\widehat{A_1}+\widehat{A_2}+\widehat{A_3}=180^o\) ( góc bẹt )
\(\Rightarrow\widehat{A_1}+\widehat{A_3}=90^o\left(\widehat{A_2}=90^o\right)\) (1)
Trong \(\Delta CAK\left(\widehat{K_1}=90^o\right):\widehat{A_3}+\widehat{C_1}=90^o\) (2)
Từ (1) và (2) \(\Rightarrow\widehat{A_1}=\widehat{C_1}\)
Xét \(\Delta HAB,\Delta KCA\) có:
\(\widehat{A_1}=\widehat{C_1}\left(cmt\right)\)
\(\widehat{H_1}=\widehat{K_1}=90^o\)
AB = AC ( gt )
\(\Rightarrow\Delta HAB=\Delta KCA\) ( c.huyền - g.nhọn )
\(\Rightarrow BH=AK;HA=CK\) ( các cạnh t/ứng )
Áp dụng định lí Py-ta-go vào \(\Delta ACK\left(\widehat{K_1}=90^o\right)\) ta có:
\(AK^2+CK^2=AC^2\)
\(\Rightarrow BH^2+CK^2=AC^2\)
\(\Rightarrow BH^2+CK^2\) có giá trị không đổi ( đpcm )
Vậy...
tam giac ABC vuong tai a co AB=AC.duong thang d di qua A sao cho B va C nam cung phia doi voi d .ke BH va CKcung vuong goc voi d .Biet bh = 5 cm .CK = 2cm . HK =?
CO HINH VE MINH HOA THI MINH CAM ON NHA
cho tam giac abc vuong can tai a,ab =3 cm .qua a ke duong thang d ko cat canh bc.ke bh vuong goc voi d tai h,ck vuong goc voi d tai k
a) chung minh bh song song ck
b)tinh do dai canh bc va so do g minh
c)chung minh goc hab = goc ack
d)chung minh bh +ck =hk
cac ban thong cam ,t ko viet dc dau
cho tam giac ABC can tai A . Ve BH vuong goc voi AC (H thuoc AC) ,CK vuong goc voi AB(K thuoc AB) a/chung minh rang AH=AK b/ goi i la giao diem cua BH va CK .chung minh ^KAI=^HAI c/duong thang AC cat BC tai P .chung minh AI vuong goc voi BC tai P
Cau 1: Cho tam giac ABC cuong tai A, AB=8cm; AC=15cm. Ve duong cao AH
a) chung minh AB^2= BH. BC
b) Tinh BH, CH, AH, BC
c) Ve phan giac AD cua tam giac ABC. Chung minh H nam giua B va D
d) Tinh ti so dien tich D HAC va D A.BC
Cau 2: Cho tam giac ABC vuong tai A, AB=5cm; Ac=12cm, ve duong cao AH va duong phan giac AD.
a) Tinh BC, BD
b) Chung minh D ACH: D ABC; tinh AH
c) Qua B ke duong thang vuong goc voi AB cat tia AD tai K. Chung minh AB.AD =AC. KD
.Cau 3: Cho tam giac ABC vuong A co AB = 5cm; AC=12cm. Ve dcao AH va pgiac AD cua goc BAC
a) Tih BC; BD
b) Chung minh D HAC : D ABC
c) Qua B ke duong vgoc voi BA cat AD tai k. Chung minh AB.AD= AC.KD
Tam giac ABC nhon co AB < AC . Ke AH vuong goc voi BC tai H . Ve phia ngoai tam giac ABC ve doan thang BD vuong goc voi AB , BD = AB va CE vuong goc voi AC , CE = AC . Ke DM vuong goc voi duong thang BC tai M va EN vuong goc voi duong thang BC tai N
1, So sanh goc DBM voi goc BAH , goc ECN voi goc CAH
2, Chung minh : DM = BH va EN = CH