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
ta có góc DAC= góc DAB+ góc BAC= 90 độ+ góc BAC
góc BAE= góc BAC+ góc EAC= 90 độ+ góc BAC
=> góc DAC= góc BAE
xét tam giác DAC và tam giác BAE có:
góc DAC= góc BAE
AD=AB
AE=AC
=> △DAC=△BAE(c.g.c)
=> góc ADC= góc ABE và DC=BE
gọi giao của DC với AB là K và giao của DC với BE là I
=> góc ADC+ góc AKD= 90 độ
mà góc AKD= góc IKB và góc ADC= góc ABE
=> góc IKB+ góc ABE= 90 độ hay
góc IKB+ góc KBI= 90 độ
=> △IKB vuông
=> DC⊥BE
xét tam giác EDC có:
M là trung điểm DE
P là trung điểm CE
=> MP là đường trung bình của tam giác EDC
=> MP//DC và MP=\(\frac12DC\)
CMTT: => NM là đường trung bình của tam giác DBE
=> NM//BE và \(NM=\frac12BE\)
mà BE=CD
từ các điều trên => NM=MP
=> tam giác NMP cân tại M
ta NM//BE và MP//DC lại có DC⊥BE
=> NM⊥MP
=> tam giác MNP vuông cân tại M(đpcm)
ta có góc DAC= góc DAB+ góc BAC= 90 độ+ góc BAC
góc BAE= góc BAC+ góc EAC= 90 độ+ góc BAC
=> góc DAC= góc BAE
xét tam giác DAC và tam giác BAE có:
góc DAC= góc BAE
AD=AB
AE=AC
=> △DAC=△BAE(c.g.c)
=> góc ADC= góc ABE và DC=BE
gọi giao của DC với AB là K và giao của DC với BE là I
=> góc ADC+ góc AKD= 90 độ
mà góc AKD= góc IKB và góc ADC= góc ABE
=> góc IKB+ góc ABE= 90 độ hay
góc IKB+ góc KBI= 90 độ
=> △IKB vuông
=> DC⊥BE
xét tam giác EDC có:
M là trung điểm DE
P là trung điểm CE
=> MP là đường trung bình của tam giác EDC
=> MP//DC và MP=\(\frac12DC\)
CMTT: => NM là đường trung bình của tam giác DBE
=> NM//BE và \(NM=\frac12BE\)
mà BE=CD
từ các điều trên => NM=MP
=> tam giác NMP cân tại M
ta NM//BE và MP//DC lại có DC⊥BE
=> NM⊥MP
=> tam giác MNP vuông cân tại M(đpcm)
một bài toán có thể giúp cho một số bài, chúc các câu học tốt còn acc trên lỡ dùng acc phụ:v