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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 )
3b)
Ta có tg BNK vuông tại K ->BN>BK
Ta có IK=MN(tính chất đoạn chắn)
Ta có : BC+MN=BK+KC+MN=BK+BI+IK=2BK
Vì BK<BN->2BK<2BN->BN>BK/2->BN>BC+MN/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)
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