Cho tam giác ABC. Vẽ ra phía ngoài tam giác đó các điểm D,E sao cho DB vuông góc AB, DB=AB ,CE vuông góc AC, CE=AB. Vẽ AH vuông góc với BH(HϵBC) CK vuông góc BE tại K, AH cắt CK tại N. Chứng minh: a)NA=NB
b) NB vuông góc CD
cho tam giác abc vuông tại a (ab<ac ),đường cao ah.Về phía ngoài tam giác abc vẽ tam giác ace vuông cân tại c.Kẻ en vuông góc bc(n thuộc bc)
a) chứng minh tam giác ahc = cne
b) đường thẳng vuông góc với ce tại e cắt ab,ah lần lượt tại i;k.Hỏi tam giác aic là tam giác gì?Vì sao
c) chứng minh ak=bc
d) chứng minh be vuông góc ck
Cho tam giác ABC vuông tại A ( AB < AC ), đường cao AH. Về phía ngoài tam giác ABC vẽ tam giác vuông ACE cân tại C. Kẻ EN vuông góc với BC ( N thuộc BC ) a. Chứng minh tam giác AHC= tam giác CNE b. Đường thẳng vuông góc với CE tại E cắt các đường thẳng AB, Ah lần lượt là I, K. Hỏi tam giác AIC là tam giác gì, vì sao c. Chứng minh AK= BC d. CM BE vuông góc vs CK Mình mong mọi người làm giúp mình nhaa❤️🙆
a) Xét tam giác ABC và ADE vuông tại A
+) AB=AD
+) AC=AE
=> tam giác ABC bằng tam giác ADE
=> BC= DE
b)
TA có tam giác ABD và ACE đều vuông cân tại A
=> góc ABD = ADB= ACE=AEC = 45
=> BD//CE (có 2 góc so le trong bằng nhau)
c) Gọi đường NA cắt MC tại I
Xét tam giác NMC có 2 đường cao MH và NI cắt nhau tại A
=> A là trực tâm tam giác NMC
=> CA là đường cao thứ ba
=> CA ⊥ MN
d)
Ta chứng minh được tam giác ADM và AME cân tại M
Suy ra MD=MA và MA=ME
=> MD=ME=MA
=> MA=DE/2
Cho tam giác ABC, có AB = AC ( góc A < 90 độ ). Vẽ BH vuông góc với AC tại H, CK vuông góc với AB tại K ( H thuộc AC, K thuộc AB ). a) chứng minh AH = AK. b) Gọi I là giao điểm của BH và CK. Chứng minh rằng tam giác IBK = tam giác ICH. c) chứng minh AI là phân giác của góc A. d) Gọi M là trung điểm của BC. Chứng minh ba điểm A,I,M thẳng hàng.
Cho tam giác ABC, có AB = AC ( góc A < 90 độ ). Vẽ BH vuông góc với AC tại H, CK vuông góc với AB tại K ( H thuộc AC, K thuộc AB ). a) chứng minh AH = AK. b) Gọi I là giao điểm của BH và CK. Chứng minh rằng tam giác IBK = tam giác ICH. c) chứng minh AI là phân giác của góc A. d) Gọi M là trung điểm của BC. Chứng minh ba điểm A,I,M thẳng hàng.
a: Xét ΔAHB vuông tại H và ΔAKC vuông tại K có
AB=AC
\(\widehat{BAH}\) chung
Do đó: ΔAHB=ΔAKC
=>AH=AK
b: Ta có: ΔAHB=ΔAKC
=>\(\widehat{ABH}=\widehat{ACK}\)
=>\(\widehat{KBI}=\widehat{HCI}\)
Ta có: AK+KB=AB
AH+HC=AC
mà AK=AH và AB=AC
nên KB=HC
Xét ΔIKB vuông tại K và ΔIHC vuông tại H có
KB=HC
\(\widehat{KBI}=\widehat{HCI}\)
Do đó: ΔIKB=ΔIHC
c: ta có: ΔIKB=ΔIHC
=>IB=IC
Xét ΔABI và ΔACI có
AB=AC
BI=CI
AI chung
Do đó: ΔABI=ΔACI
=>\(\widehat{BAI}=\widehat{CAI}\)
=>AI là phân giác của góc BAC
d: Ta có: AB=AC
=>A nằm trên đường trung trực của BC(1)
ta có: IB=IC
=>I nằm trên đường trung trực của BC(2)
ta có: MB=MC
=>M nằm trên đường trung trực của BC(3)
Từ (1),(2),(3) suy ra A,I,M thẳng hàng
Bài 6 (các câu khác nhau thì không liên quan đến nhau)
a) Cho tam giác ABC, kẻ BH AC ( H AC); CK AB ( K AB). Biết BH = CK.
Chứng minh tam giác ABC cân.
Tết đến tưng bừng, vui mừng làm Toán
Giáo viên: Nguyễn Cao Uyển Mi
b) Cho Tam giác ABC, gọi M, N lần lượt là trung điểm các cạnh AB, AC. Biết CM =
BN. Chứng tỏ tam giác ABC cân.
c) Cho tam giác ABC cân tại A, Tia phân giác của góc B và góc C cắt AC và AB lần
lượt tại D và E. Chứng minh BD = CE.
Bài 7: Cho tam giác ABC cân tại A. Trên tia đối của tia BC lấy điểm D, trên tia đối của tia
CB lấy điểm E sao cho BD = CE. Kẻ BH vuông góc với AD tại H, CK vuông góc với AE
tại K. Hai đường thẳng HB và KC cắt nhau tại I. Chứng minh rằng:
a) Tam giác ADE cân.
b) Tam giác BIC cân.
c) IA là tia phân giác của góc BIC.
Bài 8: Cho tam giác ABC vuông tại A, có AB = 5cm, BC = 13cm. Kẻ AH vuông góc với
BC tại H. Tính độ dài các đoạn thẳng: AC, AH, BH, CH.
Bài 9: (các câu khác nhau thì không liên quan đến nhau)
a) Cho tam giác ABC vuông tại A, đường cao AH = 2cm. Tính các cạnh của tam giác
ABC biết: BH = 1cm, HC = 3cm.
b) Cho tam giác ABC đều có AB = 5cm. Tính độ dài đường cao BH?
Bài 10: Cho tam giác ABC có góc A nhỏ hơn 900. Vẽ ra phía ngoài tam giác ABC các
tam giác vuông cân đỉnh A là MAB, NAC.
a) Chứng minh: MC = NB.
b) Chứng minh: MC NB
c) Giả sử tam giác ABC đều cạnh 4 cm. Tính MB, NC và chứng minh MN // BC.
Giúp mình với ạ, mik đang cần gấp
Ai giúp mik với mik đang cần gấp ạ
Cho tam giác ABC cân tại A. Kẻ BH vuông góc với AC, CK vuông góc với AB ( H thuộc AC,K thuộc AB. 1) Chứng minh: BH =CK . 2) Trên tia đối CA lấy điểm E sao cho CE=CH . Kẻ KM vuông góc với BC tại M và EN vuông góc với BC tại N. Gọi I là giao điểm của KE với cạnh BC.Chứng minh EN = KM và I là trung điểm của KE
Cho tam giác cân ABC tại A. Vẽ BH vuông góc với AC tại H và CK vuông góc với AB tại K.
1) Chứng minh tam giác ABH= tam giác ACK
2) Gọi O là giao điểm của BH và CK. Chứng minh OB=OC
3) Chứng minh HK//BC
4) Trên tia đối của CA lấy E sao cho CE=CH. Gọi I là giao điểm của EK và BC. Chứng minh I là trung điểm của EK.
( Mình đang cần gấp, b nào biết giải giúp mình với, mình cảm ơn nhiều ạ :33)
1) Xét ΔABH vuông tại H và ΔACK vuông tại K có
AB=AC(ΔABC cân tại A)
\(\widehat{BAH}\) chung
Do đó: ΔABH=ΔACK(Cạnh huyền-góc nhọn)
2) Xét ΔBCK vuông tại K và ΔCBH vuông tại H có
BC chung
CK=BH(ΔABH=ΔACK)
Do đó: ΔBCK=ΔCBH(Cạnh huyền-cạnh góc vuông)
Suy ra: \(\widehat{KCB}=\widehat{HBC}\)(hai góc tương ứng)
hay \(\widehat{OBC}=\widehat{OCB}\)
Xét ΔOBC có \(\widehat{OBC}=\widehat{OCB}\)(cmt)
nên ΔOBC cân tại O(Định lí đảo của tam giác cân)
Suy ra: OB=OC
3) Ta có: ΔACK=ΔAHB(cmt)
nên AK=AH(hai cạnh tương ứng)
Xét ΔABC có
\(\dfrac{AK}{AB}=\dfrac{AH}{AC}\)
nên HK//BC(Định lí Ta lét đảo)
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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vẽ tam giác ABC . vẽ BD vuông góc với BC , D thuộc AC , CE vuông góc AB , E thuộc AB . trên tia đối BD , lấy H : BH=AC . trên tia đối CE , lấy K : CK = AB . chứng minh rằng AH = Ak