Cho tam giác ABC vuông cân tại A, từ A kẻ đường thẳng d nằm ngoài tam giác ABC, kẻ BD vuông góc với d, CE cũng vuông góc với d; gọi M là TĐ của BC. CMR tam giác MDE vuông cân.
Cho tam giác ABC vuông tại A có AB = AC. Qua A kẻ đường thẳng d ở ngoài tam giác ABC. Vẽ BD và CE vuông góc với d. M là trung điểm BC. Chứng minh rằng:
a. BD + CE = DE?
b. Tam giác MDE vuông cân?
Cho tam giác ABC vuông cân tại đỉnh A. Một đường thẳng d đi qua A nhưng không đi qua miền trong tam giác. Kẻ BD vuông góc với đường thẳng d tại D; kẻ CE vuông góc với đường thẳng d tại E
CMR:
- BD + CE = DE
- Gọi I là trung điểm của BC. CMR: Tam giác DIE vuông cân
dòng cuối: em sửa lại kết luận: tam giác DIE vuông nhé!
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
Cho tam giác ABC vuông cân tại A. Qua A vẽ một đường thẳng d ở ngoài tam giác ABC. Vẽ BD vuông góc với d tại D,CE vuông góc với d tại E . M là trung điểm của BC. Cmr
A.BD+CE=DE
B.∆MDE vuông cân
Khó quá!Hu hu hu
CM TAM GIÁC MDE VUÔNG CÂN
CÁC BẠN NHOWS D CĂT BC NHAAAAAAAAAAAAAAAAAAA
Mình nghĩ M là trung điểm của BC.
Xét tam giác MAE và tam giác MBD có: MA = MB (do tam giác ABC vuông cân tại A), AE = BD (chứng minh trên), \(\widehat{MBD}=\widehat{MAE}\).
Do đó \(\Delta MAE = \Delta MBD(c.g.c)\Rightarrow MD=ME; \widehat{AME}=\widehat{BMD})\Rightarrow MD=ME; \widehat{EMD}=\widehat{AMB}=90^o\Rightarrow\text{Tam giác MDE vuông cân tại M}\).
Ta có \(\Delta ADB=\Delta CEA\left(g.c.g\right)\)
\(\Rightarrow BD=EA\).
Do đó \(BD^2+CE^2=EA^2+CE^2=AC^2\) không đổi.
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 cân tại A, d là đường thẳng bất kì đi qua A (d không cắt đoạn BC). Từ B và C kẻ BD và CE cùng vuông góc với d.
a) CMR: BD//CE.
b). CMR: tam giác ADB = tam giác CEA.
c) CMR: BD + CE= DE.
d) Gọi M là trung điểm của BC. CMR: tam giác DAM = tam giác ECM và tam giác DME vuông cân.
Cho tam giác ABC vuông cân tại A. Qua A kẻ đường thẳng d tuỳ ý. Từ B và C kẻ BH và CK vuông góc với d. Chứng minh rằng BH2 CK2 không phụ thuộc vào vị trí của đường thẳng d.vẽ BD vuông góc d tại D, CE vuông góc d tại E. CMR DE = BD+CE, BD2+CE2=AB2
gọi M là trung điểm của cạnh BC. CMR tam giác DME là tam giác vuông cân
Cho tam giác ABC vuông cân tại A, d là đường thẳng bất kì qua A (d không cắt đoạn BC).Từ B và C kẻ BD và CE cùng vuông góc với d
a) CMR: BD//CE
b)tam giác ADB = tam giác CEA
c)BD+CE=DE
d) gọi M là trung điểm BC. CMR tam giacsDAM=tam giác ECM và tam giác DME vuông cân
a) Ta có BD và CE đều vuông góc với d
Nên góc CEA=góc BDA (=90 độ)
Mà 2 góc này ở vị trí đồng vị
Nên BD//CE
b) Ta có d// BC
---------> góc ECB=góc DBC=góc CED ( =90 dộ )
Nên ECDB là HCN
Mà ABC là vuông cân nên góc ECA=góc DBA= 45 độ
-------->tam giác CEA = tam giác DBA ( cạnh huyền góc nhọn)
c)( mình lười bấm quá nên mình làm tắt nha)
Chứng minh góc CAE= góc BAD ( do góc ECA= góc DBA và góc ACB=góc EAC=45 độ do ED//BC)
Nên CE=EA và DB=AD, mặt khác AE=AC ( do 2 tam giác bằng nhau cm câu b)
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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