Cho tam giác ABC vuông tại B, M trên tia đối của t là trung điểm của BC trên tia AM lấy E sao cho ME = MA chứng minh rằng
a. Tam giác ABM = tam giác ECM
b.BC vuông góc với CE
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Cho tam giác ABC vuông tại B , M trên tia đối của t là trung điểm của BC. Trên tia AB lấy E sao cho MA=ME chứng minh rằng
a.Tam giác ABM bằng tam giác ECM
b BC vuông góc với CE
.
a: Xét ΔABM và ΔECM có
MA=ME
\(\widehat{AMB}=\widehat{EMC}\)
MB=MC
Do đó: ΔABM=ΔECM
b: Xét tứ giác BACE có
M là trung điểm của BC
M là trung điểm của AE
Do đó: BACE là hình bình hành
Suy ra: CE//AB
hay CE⊥BC
Diễn giải:
- Khi cộng, trừ số thập phân ta tiến hành cộng hoặc trừ các phần tương ứng của các số đó.
Ví dụ 1:
Tính 0,25 + 2,5 ta làm như sau: 5 + 0 = 5 , 2 + 5 =7, 0 + 2 = 2. Vậy 0,25 + 2,5 = 2.75
Tính 8,6 - 2,7 ta làm như sau: 6 - 7 không trừ được ta lấy 16 - 7 = 9, tiếp tục 8 - 2 trừ thêm 1 nữa tức là 8 -3 = 5. Vậy 8,6 - 2,7 = 5,9
- Với phép nhân, chia các số thập phân ta cần viết chúng dưới dạng phân số.
Lời giải:
a.
Xét tam giác $AMB$ và $EMC$ có:
$\widehat{AMB}=\widehat{EMC}$ (đối đỉnh)
$AM=EM$
$MB=MC$
$\Rightarrow \triangle AMB=\triangle EMC$ (c.g.c)
b.
Vì $\triangle AMB=\triangle EMC$ nên $\widehat{MAB}=\widehat{MEC}$
Mà 2 góc này ở vị trí so le trong nên $EC\parallel AB$
Mà $AB\perp AC$ nên $EC\perp AC$ (đpcm)
c.
Vì $\triangle AMB=\triangle EMC$ nên:
$AB=EC$
Vì $EC\perp AC$ nên $\widehat{ECA}=90^0=\widehat{BAC}$
Xét tam giác $ECA$ và $BAC$ có:
$\widehat{ECA}=\widehat{BAC}=90^0$ (cmt)
$AC$ chung
$EC=BA$ (cmt)
$\Rightarrow \triangle ECA=\triangle BAC$ (c.g.c)
$\Rightarrow EA=BC$
Mà $EA=2AM$ nên $2AM=BC$ (đpcm)
Cách 1: Giải theo phương pháp bậc tiểu học (của bạn Ác Quỷ)
Ta có
Mà dt(AMN) = 1/4 dt(ABN) = 1/4 . 1/2 dt(ABC) = 1/8 dt(ABC)
dt(DMN) = dt(ABC) - dt(AMN) - dt(BDM) - dt(CDN) = dt(ABC) - 1/8 dt(ABC) - 3/8 dt(ABC) - 1/4 dt(ABC) = 1/4 dt(ABC)
Vậy , suy ra AE/AD = 1/3
Cách 2: Giải theo phương pháp bậc THCS (của bạn Lê Quang Vinh)
DN là đường trung bình của tam giác ABC => DN // AB và DN = 1/2 AB
DN // AB => Hai tam giác EAM và EDN đồng dạng => EA/ED = AM/DN = 1/2 (vì AM = 1/4 AB, DN = 1/2 AB)
=> AE/AD = 1/3
a: Xét ΔABM và ΔACM có
AB=AC
AM chung
BM=CM
Do đó: ΔABM=ΔACM
\(a,\left\{{}\begin{matrix}MB=MC\\AB=AC\\AM\text{ chung}\end{matrix}\right.\Rightarrow\Delta ABM=\Delta ACM\left(c.c.c\right)\\ b,\left\{{}\begin{matrix}AM=ME\\BM=MB\\\widehat{AMB}=\widehat{EMC}\left(đđ\right)\end{matrix}\right.\Rightarrow\Delta AMB=\Delta EMC\left(c.g.c\right)\\ \Rightarrow\widehat{ABC}=\widehat{BME}\\ \text{Mà 2 góc này ở vị trí slt nên }AB\text{//}EC\\ c,\Delta AMB=\Delta AMC\\ \Rightarrow\widehat{AMB}=\widehat{AMC}\widehat{AMC}\\ \text{Mà }\widehat{AMC}+\widehat{AMB}=180^0\\ \Rightarrow\widehat{AMC}=\widehat{AMB}=90^0\\ \Rightarrow AM\bot BC\)
a) Xét ΔMAB và ΔMEC có
MA=ME(gt)
ˆAMB=ˆEMCAMB^=EMC^(hai góc đối đỉnh)
MB=MC(M là trung điểm của BC)
Do đó: ΔMAB=ΔMEC(c-g-c)
a: Xét ΔAMB và ΔAMC có
AM chung
MB=MC
AB=AC
Do đó: ΔAMB=ΔAMC
=>\(\widehat{AMB}=\widehat{AMC}\)
mà \(\widehat{AMB}+\widehat{AMC}=180^0\)(hai góc kề bù)
nên \(\widehat{AMB}=\widehat{AMC}=\dfrac{180^0}{2}=90^0\)
b: Xét ΔMBA vuông tại M và ΔMCD vuông tại M có
MB=MC
MA=MD
Do đó: ΔMBA=ΔMCD
=>\(\widehat{MBA}=\widehat{MCD}\)
mà hai góc này là hai góc ở vị trí so le trong
nên AB//CD
c: Xét ΔBEM vuông tại E và ΔCFM vuông tại F có
MB=MC
\(\widehat{MBE}=\widehat{MCF}\)
Do đó: ΔBEM=ΔCFM
=>ME=MF
ΔBEM=ΔCFM
=>\(\widehat{BME}=\widehat{CMF}\)
mà \(\widehat{BME}+\widehat{EMC}=180^0\)(hai góc kề bù)
nên \(\widehat{CMF}+\widehat{EMC}=180^0\)
=>F,M,E thẳng hàng
mà MF=ME
nên M là trung điểm của EF
Lời giải:
a. Xét tam giác $ABM$ và $ECM$ có:
$AM=EM$ (gt0
$BM=CM$ (do $M$ là trung điểm $BC$)
$\widehat{AMB}=\widehat{EMC}$ (đối đỉnh)
$\Rightarrow \triangle ABM=\triangle ECM$ (c.g.c)
b.
Từ tam giác bằng nhau phần a suy ra $\widehat{ECM}=\widehat{ABM}=90^0$
$\Rightarrow EC\perp MC$ hay $EC\perp BC$ (đpcm)
Hình vẽ:
![](data:image/png;base64,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)