cho tam giác abc cân tại a,vẽ bd vuông góc với ac tại e;cd vuông góc với ab tại d.
a)CMR:tam giác ade cân tại a.
b)giả sử be cắt cd tại h.CMR ah là tia phân giác góc bac.
c)CMRde//bc.
d)gọi m là trung điểm bc.CMR :a,h,m thẳng hàng
Những câu hỏi liên quan
1. Cho tam giác ABC vuông ở A có AB<AC. AH vuông góc với BC tại H, D là điểm trên cạnh BC sao cho AD=AB. Vẽ DE vuông góc với BC tại E. Chứng mih rằng AH=HE.
2. Cho tam giác ABC vuông cân tại A.. Qua A vẽ đường thẳng d ở ngoài tam giác ABC . Vẽ BD vuông góc với d taị D. CE vuông góc với d tại E. M là trung điểm CB. Chứng minh rằng:
a) BD + CE = DE
b) Tam giác MDE là tam giác vuông cân
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CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCGCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
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cho tam giác ABC cân tại A vẽ AH vuông góc BC tại H . Vẽ HD vuông góc vớ AB tại D , HE vuông góc với AC tại E. chứng minh Bd = CE
mà thằng hiếu nhá,ko nick nào tao kb với mày đâu
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Cho tam giác ABC vuông tại A (AB < AC), BD là đường phân giác. Vẽ DE vuông góc với BC tại E.
a) Cho biết AB = 6cm, AC = 8cm. Tính BC.
b) Chứng minh tam giác DAE cân.
c) Chứng minh rằng DA < DC.
d) Vẽ CF vuông góc với BD tại F. Chứng minh rằng các đường thẳng AB, DE, CF đồng quy.
cho tam giác ABC cân tại A . Vẽ AH xuông góc với BC tại H . Vẽ HD vuông góc với AB tại D , HE vuông góc với AC tại E . chứng minh rằng
a) BH = HC
b) BD = CE
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
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Cho tam giác ABC vuông cân ( AB=AC ). Qua A vẽ đường thẳng d ngoài tam giác ABC. Vẽ BD vuông góc với d tại D, CE vuông góc với d tại E. M là trung điểm BC. Chứng minh rằng:
a) BD+CE=DE
b) Tam giác MDE là tam giác vuông cân
cho tam giác ABC vuông tại A,vẽ tia phân giác góc B cắt AC tại D ,qua A vẽ đường thẳng vuông góc với BD catx BD tại H và cắt BC tại E
a) chứng minh tam giác ABC cân tại B
b) chứng minh DE vuông góc BC
c) chứng minh góc ABE bằng góc EDC
d) so sánh AD và DC
e) quan A vẽ đường thẳng // BD cắt BC tại F.chứng minh tam giác ABF là tam giác cân suy ra B là trung điểm EF
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
cho tam giác ABC , vẽ BE vuông góc AC tại E , vẽ CF vuông góc với AB tại F . Cho BE + AC = BA + CF . CMR tam giác ABC cân tại A
Trên tia đối của BE lấy điểm M sao cho BM=AC
Trên tia đố của CF lấy điểm N sao cho CN=AB.
Ta có: ^ABE+^BAE=^ABE+^BAC=900 (vì tam giác AEB vuông tại E)
Tương tự: ^ACF+^CAF=^ACF+^BAC=900
=> ^ABE=^ACF => 1800 - ^ABE = 1800 - ^ACF => ^MBA=^ACN
Xét \(\Delta\)BMA và \(\Delta\)CAN:
BM=AC
^MBA=^ACN => \(\Delta\)BMA=\(\Delta\)CAN (c.g.c)
AB=CN
=> MA=AN (2 cạnh tương ứng)
Lại có: BE+AC=BA+CF (giả thiết). Thay AB=CN, AC=BM, ta được:
BE+BM=CN+CF => EM=FN
Xét \(\Delta\)AEM và \(\Delta\)AFN:
AM=AN (cmt)
^AEM=^AFN=900 => \(\Delta\)AEM=\(\Delta\)AFN (Cạnh huyền cạnh góc vuông)
EM=FN
=> ^AME=^ANF (2 góc tương ứng) hay ^AMB=^ANC (1)
Mà \(\Delta\)BMA=\(\Delta\)CAN (cmt) => ^AMB=^NAC (2)
Từ (1) và (2) => ^ANC=^NAC => \(\Delta\)ACN cân tại C => AC=CN.
Mà CN=AB => AB=AC => \(\Delta\)ABC cân tại A (đpcm).
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3 tháng 4 2022 lúc 19:29
Câu 5: Cho ABC vuông tại A (AB < AC).Tia phân giác góc ABC cắt AC tại D;vẽ DE
vuông góc BC tại E
a/ Chứng minh tam giác SAD = tam giác BED
b/ AE cắt BD tại H.Chứng minh tam giác BAE cân và H là trung điểm AE
c/ Qua E vẽ đường thẳng song song BD cắt AC tại F;FH cắt DE tại G.Chứng minhDE = 3GD
a: Xét ΔBAD vuông tại A và ΔBED vuông tại E có
BD chung
góc ABD=góc EBD
=>ΔBAD=ΔBED
b: ΔBAD=ΔBED
=>BA=BE và DA=DE
=>ΔBAE cân tại B và BD là trung trực của AE
=>H là trung điểm của AE
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cho tam giác ABC vuông tại A, vẽ tia phân giác góc B cắt AC tại D, qua A vẽ đường thẳng vuông góc với BD cắt BD tại H và cắt BC tại E.
a-C/m tam giác ABE cân tại B
b-C/m DE Vuông góc với BC
c-C/m góc ABE bằng góc EDC
d-So sánh AD và DC
e-Qua A vẽ đường thẳng song song với BD cắ BC tại F. C/m tam giác ABF là tam giác cân =>B là trung điểm EF
*CẦN GẤP_K CẦN VẼ HÌNH