Cho tam giác ABC cân tại A, vẽ AH vuông góc với BC tại H, vẽ HD vuông góc với AB tại D, HE vuông góc với AC tại E. CMR :
a, AH = HC
b, BD = CE
K
Khách
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Những câu hỏi liên quan
27 tháng 7 2023
a: Xét ΔAHB vuông tại H và ΔAHC vuông tại H có
AB=AC
AH chung
=>ΔAHB=ΔAHC
=>HB=HC
b: Xét ΔHDB vuông tại D và ΔHEC vuông tại E có
HB=HC
góc B=góc C
=>ΔHDB=ΔHEC
=>BD=CE
23 tháng 3 2016
1.
Ta có : AC<AD (vì : D là tia đối của tia BC )
=> HD<HC
3.
Ta có : AB+AC>AH (vì : tog 2 cah cua tam giác luôn lớn hơn cah con lại)
Mà : 1/2AH<AB+AC
=> AB+AC>2AH
4.
Ta có : ko hiu
CL
13 tháng 2 2016
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CV
7 tháng 3 2017
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCGCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
HA
8 tháng 3 2020
TA CÓ \(\Delta ABC\)CÂN TẠI A
\(\Rightarrow\hept{\begin{cases}AB=AC\\\widehat{B}=\widehat{C}\end{cases}}\)
A) VÌ AH VUÔNG GÓC VỚI BC
=> AH LÀ ĐƯỜNG CAO
MÀ TRONG TAM GIÁC CÂN ĐƯỜNG CAO CŨNG CHÍNH LÀ ĐƯỜNG TRUNG TUYẾN
=> AH LÀ TRUNG TUYẾN CỦA BC
=> BH=CH(ĐPCM)
B) XÉT TAM GIÁC NHA
LT
8 tháng 3 2020
Vì tam giác ABC cân tại A suy ra AB=AC, góc B=góc C
Xét tam giác ABH và tam giác ACH
có AB=AC(CMT)
góc AHC=góc AHB (=900)
góc B=góc C
suy ra tam giác ABH = tam giác ACH (cạnh huyền-góc nhọn)
suy ra BH=CH (hai cạnh tương ứng)
b) Xét tam giac BHD và tam giác CHE
có BH=CH (CMT)
góc B=góc C
góc HDB = góc HEC = 900
suy ra tam giac BHD = tam giác CHE (cạnh huyền-góc nhọn)
suy ra BD=CE (hai cạnh tương ứng)