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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 )

8 tháng 3 2017

A B C M D E I 1 2

a ) Xét ∆ BDM và ∆ CEM có :

∠D = ∠E = 900 (gt)

BM = MC (gt)

∠M1 = ∠M2 ( đối đỉnh )

=> ∆ BDM = ∆ CEM ( CH - GN )

=> BD = CE ; DM = EM ( Cạnh tưng ứng )

b ) Trên tiam AM lấy điểm I sao cho AM = MI 

Xét ∆ ABM và ∆ ICM có :

AM = MI (gt)

∠M1 = ∠M2 ( đối đỉnh )

BM = MC (gt)

=> ∆ ABM = ∆ ICM (c - g - c)

=> AB = CI ( Cạnh tưng ứng )

∆ ACI có AC + CI > AI ( bđt tam giác)

Mà AM = 1/2AI => AC + CI > 2AM

Mà AB = CI (cm trên) => AB + AC > 2AM (đpcm)

6 tháng 2 2016

vẽ hình nha bạn

ghi từng bài thui

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

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

14 tháng 1 2023

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13 tháng 2 2016

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7 tháng 3 2017

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