1. Cho tam giác ABC vuông cân tại A. H là trung điểm cạnh BC. M là điểm nằm giữa B và H. Vẽ MD\(\perp\)AB tại D, ME\(\perp\)AC tại E. Chứng minh rằng AD=CE, BD=AE
Cho tam giác ABC cân tại A. Trên cạnh BC lấy D, E (D nằm giữa B và E) sao cho BD=CE. Vẽ DM\(\perp\)AB tại M, EN\(\perp\)AC tại N. Gọi K là giao điểm của MD và NE. Chứng minh rằng;
a) △MBD=△NCE; b)△MAK=△NAK
a, Xét tam giác MBD và tam giác NCE ta có :
DM = CE (gt)
^MBD = ^NCE (gt)
Vậy tam giác MBD = tam giác NCE ( ch - gn )
=> MB = NC ( 2 cạnh tương ứng )
=> AM = AN
b, Xét tam giác MAK và tam giác NAK có :
AK _ chung
AM = AN ( cmt )
Vậy tam giác MAK = tam giác NAK ( ch - cgv )
Cho ΔABC vuông cân tại A. H là trung điểm của BC. M là điểm nằm giữa B và H. Vẽ MD ⊥ AB tại D, ME ⊥ AC tại E. Chứng minh rằng:
a) AH ⊥ BC
b) AD = CE, BD = AE
c) MB^2 + MC^2 = MA^2
cho tam giác abc vuông cân tại a. h là trung điểm cạnh bc. m là trung điểm cạnh bc. m là điểm nằm giữa b và h. vẽ md vuông góc ab tại d, me vuông góc với ac tại e. Cm:
a) ah vuông góc với bc
b) ad= ce, bd= ae
c) mb mũ 2 + mc mũ 2= 2ma mũ 2
Cho ΔABC vuông cân tại A. H là trung điểm của cạnh BC. M là điểm nằm giữa B và H. Vẽ MD ⊥ AB tại D, ME ⊥ AC tại E. Chứng minh rằng:
a) AH ⊥ BC
b) AD = CE, BD = AE
c) MB2 + MC2 = 2MA2
Nhanh lên nhé! Mk đang cần gấp
cho tam giác ABC vuông cân tại A. H là trung điểm cạnh BC.M là điểm nằm giữa B và H. Bẽ MD vuông góc AB tại D, ME vuông góc AC tại E .chứng minh rằng : a, AH vuông góc BC
b, ADb= CE , BD = AE
c, MB2 + MC2 = 2MA2
1.Cho tam giác ABC vuông tại A (AB>AC)
a) Cho biết AB= 8cm, BC= 10cm. Tính AC.
b) Gọi M là trung điểm cạnh BC. Trên tia đối tia MA lấy D sao cho MD =MA. Vẽ AH vuông góc BC tại H, trên tia đối của tia HA lấy E sao cjo HE=HA. Cứng minh rằng:
*CD vuông góc AC *tam giác CAEcân *BD=CE *AE vuông góc ED
2.Cho tam giác ABC vuông cân tại A. H là trung điểm cạnh BC. M là điểm nằm giữa B và H. Vẽ MD vuông góc AB tại D, ME vuông góc AC tại E. Chứng minh rằng:
a)AH vuông góc BC b) AD=CE, BD=AE c) MB2 + MC2 = 2MA2
Mình cần gấp, các bạn giải nhanh và đầy đủ giúp mình nhé, cảm ơn.
1) Cho tam giác ABC vuông tại A ( AB > AC ) . Trên tia đối của tia AC lấy điểm D sao cho AD = AB. Trên cạnh AB lấy điểm E sao cho AC = AE
a) Chứng minh rằng : tam giác ABC = tam giác ADE
b) Gọi M , N lần lượt là trung điểm của DE và BC. Chứng minh tam giác ADM = tam giác ABN và tam giác AMN vuông cân
c) Qua E kẻ EH vuông góc với BC tại H. Chứng minh rằng 3 điểm D ; E ; H thẳng hàng và CE vuông góc với BD
Xét ΔADE và ΔABC có :
AD = AB (gt)
góc DAE =góc BAC = 90 độ
AE = AC (gt)
Do đó : ΔADE = ΔABC(c − g − c)
⇒ DE = BC ( hai cạnh tương ứng )
b.
Ta có :
góc ADE =góc CDN ( hai góc đối đỉnh )
góc C= góc E
( vì ΔADE = ΔABC )
⇒ góc N = góc A 90đọ
Hay DE ⊥ BC
Vậy DE ⊥ BC
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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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cho tam giác ABC cân tại A.Trên cạnh BC lấy D,E (D nằm giữa B và E sao cho BD=CE).Vẽ DM vuông góc với AB tại M, EN vuông góc với AC tại N. gọi K là giao điểm của MD và NE. Chứng minh rằng: a) tam giác MBD = tam giác NCE. b) tam giác MAK = tam giác NAK
a: Xét ΔMBD vuông tại M và ΔNCE vuông tại N có
DB=EC
\(\widehat{DBM}=\widehat{ECN}\)(ΔABC cân tại A)
Do đó: ΔMBD=ΔNCE
b: Ta có: ΔMBD=ΔNCE
=>MB=NC
Ta có: AM+MB=AB
AN+NC=AC
mà MB=NC và AB=AC
nên AM=AN
Xét ΔAMK vuông tại M và ΔANK vuông tại N có
AK chung
AM=AN
Do đó: ΔAMK=ΔANK