Bài 5: Cho ∆ABC cân tại A .Vẽ AH vuông góc BC.
a) Chứng minh: H là trung điểm của BC.
b) Vẽ HDvuông góc AB tại D và HE vuông gócAC tại E. Chứng minh: ∆HDE cân.
c) Chứng minmh : DE//BC.
K
Khách
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Những câu hỏi liên quan
25 tháng 6 2023
a: Xét ΔAHB vuông tại H và ΔAHC vuông tại H có
AB=AC
AH chung
=>ΔAHB=ΔAHC
=>HB=HC
=>H là trung điểm của BC
b: Xét ΔAMH vuông tại M và ΔANH vuông tại N có
AH chung
góc MAH=góc NAH
=>ΔAMH=ΔANH
=>AM=AN
=>ΔAMN cân tại A
N
29 tháng 2 2020
Tự vẽ hình nhé ?
a) Vì tam giác ABC cân tại A (GT)
=> Góc ABC = ACB (định lý) (1)
Vì tam giác ABC cân tại A (GT)
=> AB = AC (định nghĩa) (2)
Xét tam giác ABD và tam giác ACD có:
Góc ADB = ADC = 90o (Vì AD vuông góc BC (GT))
AB = AC (Theo (2))
Góc ABC = ACB (Theo (1))
=> Tam giác ABD = tam giác ACD (cạnh huyền - góc nhọn) (3)
=> BD = CD (2 cạnh t.ứng)
Mà D nằm giữa B và C
=> D là trung điểm của BC (đpcm)
b) Từ (3) => Góc BAD = CAD (2 góc t.ứng) (4)
Mà AD nằm giữa AB và AC
=> AD là tia pg của góc BAC (đpcm)
c) Xét tam giác AED và tam giác AFD có :
Góc AED = AFD = 90o (Vì DE vuông góc AB, DF vuông góc AC (GT))
AD chung
Góc BAD = CAD (Theo (4))
=> Tam giác AED = tam giác AFD (cạnh huyền - góc nhọn)
=> ED = FD (2 cạnh t.ứng)
Xét tam giác DEF có ED = FD (cmt)
=> Tam giác DEF cân tại D (định nghĩa)
Vậy ...
P
4 tháng 2 2022
a) Xét △AHB và △AHC có:
AB = AC (gt)
BH = HC (gt)
AH Chung
=>△AHB = △AHC (c.c.c)
Do đó góc A1 = góc A2 (2 góc tương ứng)
Mà H là trung điểm của BC => AH vuông góc với BC
b) Xét △AHM và △AHN có:
Góc A1 = Góc A2 (cmt)
Góc M = Góc N (gt)
AH Chung
=> △AHM = △AHN (Cạnh huyền - Góc nhọn)
c) Vì △AHM = △AHN (cmt)
=> AM = AN (2 cạnh tương ứng)
Vì I là giao điểm của MH và AC, K là giao điểm của NH và AB.
=>AK = AI
Do đó: △AIK là tam giác cân (Do có 2 cạnh bằng nhau)
CL
13 tháng 2 2016
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CV
7 tháng 3 2017
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15 tháng 2 2022
a: AH=8cm
b: Xét ΔABH vuông tại H và ΔACH vuông tại H có
AB=AC
AH chung
Do đó: ΔABH=ΔACH
c: Xét ΔDBH và ΔECH
DB=EC
\(\widehat{B}=\widehat{C}\)
BH=CH
Do đó: ΔDBH=ΔECH
Suy ra: HD=HE
hay ΔHDE cân tại H
d: Ta có: AD=AE
nên A nằm trên đường trung trực của DE(1)
Ta có: HD=HE
nên H nằm trên đường trung trực của DE(2)
Từ (1) và (2) suy ra AH là đường trung trực của DE
27 tháng 5 2016
a)Xet 2 tam giác ADF va BDE có BD=AD goc ADF=goc BDE DF=DE => tam giac ADF=tam giac BDE => goc AFD= goc BFD => goc AFD=90 AF vuong goc voi FE
24 tháng 3 2021
Bài 5:
a) Áp dụng định lí Pytago vào ΔABC vuông tại A, ta được:
\(BC^2=AB^2+AC^2\)
\(\Leftrightarrow BC^2=5^2+12^2=169\)
hay BC=13(cm)
Vậy: BC=13cm
b) Xét ΔABE vuông tại B và ΔDBE vuông tại B có
EB chung
BA=BD(B là trung điểm của AD)
Do đó: ΔABE=ΔDBE(hai cạnh góc vuông)
Suy ra: EA=ED(Hai cạnh tương ứng)
Xét ΔEAD có EA=ED(cmt)
nên ΔEAD cân tại E(Định nghĩa tam giác cân)
2 tháng 3 2022
a: \(BC=\sqrt{6^2+8^2}=10\left(cm\right)\)
b: Xét ΔBCD có
BA là đường cao
BA là đường trung tuyến
Do đó: ΔBCD cân tại B