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a) Xét ∆ vuông BDM và ∆ vuông MCE ta có : 

BM = MC (gt)

DMB = CME ( đối đỉnh) 

=> ∆BDM = ∆MCE ( ch-gn)

b) => BD = EC ( 2 góc tương ứng

Ta có : DM < BM ( Trong ∆ vuông cạnh huyền luôn luôn lớn hơn cạnh góc vuông )

Mà BM = MC 

=> DM < MC ( trái đk đề bài )

6 tháng 2 2016

vẽ hình nha bạn

ghi từng bài thui

13 tháng 1 2019

chị làm đây ko bt đúng hay sai đâu nha

xét tam giác ABC có BD vuông góc với AC

                               CE vuông góc với AB 

                               hai đường thẳng này cát nhau tại I 

suy ra I là trực tâm của tam giác ABC

suy ra AI vuông góc với BC(1)

Mặt khác, M là trung điểm của BC=> AM là đường trung tuyến của tam giác ABC

mà trong 1 tam giác cân đường trung tuyến đồng thời là đường cao

<=> AM cũng là đường cao của tam giác ABC

=> AM vuông góc với BC(2)

từ (1)(2) ta có A,I,M thẳng hàng

8 tháng 4 2018

help me

9 tháng 4 2018

a) Xét tam giác vuông ADB và tam giác vuông ACE có:

Góc A chung

AB = AC (gt)

\(\Rightarrow\Delta ABD=\Delta ACE\)   (Cạnh huyền - góc nhọn)

b) Do \(\Delta ABD=\Delta ACE\Rightarrow AD=AE\)

Xét tam giác vuông AEH và tam giác vuông ADH có:

Cạnh AH chung

AE = AD (cmt)

\(\Rightarrow\Delta AEH=\Delta ADH\)   (Cạnh huyền - cạnh góc vuông)

\(\Rightarrow HE=HD\)

c) Xét tam giác ABC có BD, CE là đường cao nên chúng đồng quy tại trực tâm. Vậy H là trực tâm giác giác.

Lại có AM cũng là đường cao nên AM đi qua H.

d) Xét các tam giác vuông EBC và EAC, áp dụng định lý Pi-ta-go ta có:

\(BC^2=EB^2+EA^2;AC^2=EA^2+EC^2\)   

Tam giác ABC cân tại A nên AB = AC hay \(AB^2=AC^2\)

Vậy nên \(AB^2+AC^2+BC^2=2AC^2+BC^2=2\left(EA^2+EC^2\right)+EB^2+EC^2\)

\(=3EC^2+2EA^2+BC^2\).

13 tháng 2 2016

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7 tháng 3 2017

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