• Bước 1: Xác định các góc vuông:
• • Tam giác ABC vuông cân tại A nên ∠BAC=90∘angle cap B cap A cap C equals 90 raised to the exponent composed with end-exponent∠𝐵𝐴𝐶=90∘và AB = AC.
  • AH là đường cao nên ∠AHB=∠AHC=90∘angle cap A cap H cap B equals angle cap A cap H cap C equals 90 raised to the exponent composed with end-exponent∠𝐴𝐻𝐵=∠𝐴𝐻𝐶=90∘.
  • BE là đường phân giác của ∠ABHangle cap A cap B cap H∠𝐴𝐵𝐻nên ∠ABE=∠EBH=12∠ABHangle cap A cap B cap E equals angle cap E cap B cap H equals 1 over 2 end-fraction angle cap A cap B cap H∠𝐴𝐵𝐸=∠𝐸𝐵𝐻=12∠𝐴𝐵𝐻.
  • CF là đường phân giác của ∠ACHangle cap A cap C cap H∠𝐴𝐶𝐻nên ∠ACF=∠FCH=12∠ACHangle cap A cap C cap F equals angle cap F cap C cap H equals 1 over 2 end-fraction angle cap A cap C cap H∠𝐴𝐶𝐹=∠𝐹𝐶𝐻=12∠𝐴𝐶𝐻.
• Bước 2: Tính các góc trong tam giác ABE:
• • ∠ABH=90∘−∠BAC=90∘−90∘=0∘angle cap A cap B cap H equals 90 raised to the exponent composed with end-exponent minus angle cap B cap A cap C equals 90 raised to the exponent composed with end-exponent minus 90 raised to the exponent composed with end-exponent equals 0 raised to the exponent composed with end-exponent∠𝐴𝐵𝐻=90∘−∠𝐵𝐴𝐶=90∘−90∘=0∘.
  • ∠ABE=12∠ABHangle cap A cap B cap E equals 1 over 2 end-fraction angle cap A cap B cap H∠𝐴𝐵𝐸=12∠𝐴𝐵𝐻.
  • ∠BAC+∠ABC+∠ACB=180∘angle cap B cap A cap C plus angle cap A cap B cap C plus angle cap A cap C cap B equals 180 raised to the exponent composed with end-exponent∠𝐵𝐴𝐶+∠𝐴𝐵𝐶+∠𝐴𝐶𝐵=180∘.
  • Vì tam giác ABC vuông cân tại A nên ∠ABC=∠ACB=45∘angle cap A cap B cap C equals angle cap A cap C cap B equals 45 raised to the exponent composed with end-exponent∠𝐴𝐵𝐶=∠𝐴𝐶𝐵=45∘.
  • ∠ABC=∠ABH+∠HBC=45∘angle cap A cap B cap C equals angle cap A cap B cap H plus angle cap H cap B cap C equals 45 raised to the exponent composed with end-exponent∠𝐴𝐵𝐶=∠𝐴𝐵𝐻+∠𝐻𝐵𝐶=45∘.
  • ∠ABH=90∘−∠BAC=90∘−45∘=45∘angle cap A cap B cap H equals 90 raised to the exponent composed with end-exponent minus angle cap B cap A cap C equals 90 raised to the exponent composed with end-exponent minus 45 raised to the exponent composed with end-exponent equals 45 raised to the exponent composed with end-exponent∠𝐴𝐵𝐻=90∘−∠𝐵𝐴𝐶=90∘−45∘=45∘.
  • ∠ABE=12∠ABH=12×45∘=22.5∘angle cap A cap B cap E equals 1 over 2 end-fraction angle cap A cap B cap H equals 1 over 2 end-fraction cross 45 raised to the exponent composed with end-exponent equals 22.5 raised to the exponent composed with end-exponent∠𝐴𝐵𝐸=12∠𝐴𝐵𝐻=12×45∘=22.5∘.
  • ∠AEB=180∘−∠BAE−∠ABE=180∘−90∘−22.5∘=67.5∘angle cap A cap E cap B equals 180 raised to the exponent composed with end-exponent minus angle cap B cap A cap E minus angle cap A cap B cap E equals 180 raised to the exponent composed with end-exponent minus 90 raised to the exponent composed with end-exponent minus 22.5 raised to the exponent composed with end-exponent equals 67.5 raised to the exponent composed with end-exponent∠𝐴𝐸𝐵=180∘−∠𝐵𝐴𝐸−∠𝐴𝐵𝐸=180∘−90∘−22.5∘=67.5∘.
  • ∠BAE=90∘angle cap B cap A cap E equals 90 raised to the exponent composed with end-exponent∠𝐵𝐴𝐸=90∘.
• Bước 3: Kết luận:
• • Vì ∠BAE=90∘angle cap B cap A cap E equals 90 raised to the exponent composed with end-exponent∠𝐵𝐴𝐸=90∘, nên tam giác ABE vuông tại A. 

• Bước 1: Gọi D là giao điểm của AH và BI
• Bước 2: Chứng minh tam giác ABD vuông tại D:
• • ∠BAD=∠BAC−∠CADangle cap B cap A cap D equals angle cap B cap A cap C minus angle cap C cap A cap D∠𝐵𝐴𝐷=∠𝐵𝐴𝐶−∠𝐶𝐴𝐷.
  • ∠BAD=90∘−∠CADangle cap B cap A cap D equals 90 raised to the exponent composed with end-exponent minus angle cap C cap A cap D∠𝐵𝐴𝐷=90∘−∠𝐶𝐴𝐷.
  • ∠ABD=12∠ABC=12×45∘=22.5∘angle cap A cap B cap D equals 1 over 2 end-fraction angle cap A cap B cap C equals 1 over 2 end-fraction cross 45 raised to the exponent composed with end-exponent equals 22.5 raised to the exponent composed with end-exponent∠𝐴𝐵𝐷=12∠𝐴𝐵𝐶=12×45∘=22.5∘.
  • ∠ADB=180∘−∠BAD−∠ABD=180∘−90∘−22.5∘=67.5∘angle cap A cap D cap B equals 180 raised to the exponent composed with end-exponent minus angle cap B cap A cap D minus angle cap A cap B cap D equals 180 raised to the exponent composed with end-exponent minus 90 raised to the exponent composed with end-exponent minus 22.5 raised to the exponent composed with end-exponent equals 67.5 raised to the exponent composed with end-exponent∠𝐴𝐷𝐵=180∘−∠𝐵𝐴𝐷−∠𝐴𝐵𝐷=180∘−90∘−22.5∘=67.5∘.
  • ∠ADB=180∘−∠ADB−∠AHD=180∘−90∘−67.5∘=22.5∘angle cap A cap D cap B equals 180 raised to the exponent composed with end-exponent minus angle cap A cap D cap B minus angle cap A cap H cap D equals 180 raised to the exponent composed with end-exponent minus 90 raised to the exponent composed with end-exponent minus 67.5 raised to the exponent composed with end-exponent equals 22.5 raised to the exponent composed with end-exponent∠𝐴𝐷𝐵=180∘−∠𝐴𝐷𝐵−∠𝐴𝐻𝐷=180∘−90∘−67.5∘=22.5∘.
  • Vì ∠ABD=22.5∘angle cap A cap B cap D equals 22.5 raised to the exponent composed with end-exponent∠𝐴𝐵𝐷=22.5∘và ∠AHD=90∘angle cap A cap H cap D equals 90 raised to the exponent composed with end-exponent∠𝐴𝐻𝐷=90∘nên ∠ADB=67.5∘angle cap A cap D cap B equals 67.5 raised to the exponent composed with end-exponent∠𝐴𝐷𝐵=67.5∘.
  • Vậy ∠ABD<∠ADBangle cap A cap B cap D is less than angle cap A cap D cap B∠𝐴𝐵𝐷<∠𝐴𝐷𝐵nên ∠ADB=67.5∘angle cap A cap D cap B equals 67.5 raised to the exponent composed with end-exponent∠𝐴𝐷𝐵=67.5∘.
  • ∠BAD=90∘−∠ABD=90∘−22.5∘=67.5∘angle cap B cap A cap D equals 90 raised to the exponent composed with end-exponent minus angle cap A cap B cap D equals 90 raised to the exponent composed with end-exponent minus 22.5 raised to the exponent composed with end-exponent equals 67.5 raised to the exponent composed with end-exponent∠𝐵𝐴𝐷=90∘−∠𝐴𝐵𝐷=90∘−22.5∘=67.5∘.
  • ∠ADB=180∘−∠BAD−∠ABD=180∘−67.5∘−22.5∘=90∘angle cap A cap D cap B equals 180 raised to the exponent composed with end-exponent minus angle cap B cap A cap D minus angle cap A cap B cap D equals 180 raised to the exponent composed with end-exponent minus 67.5 raised to the exponent composed with end-exponent minus 22.5 raised to the exponent composed with end-exponent equals 90 raised to the exponent composed with end-exponent∠𝐴𝐷𝐵=180∘−∠𝐵𝐴𝐷−∠𝐴𝐵𝐷=180∘−67.5∘−22.5∘=90∘.
  • Vậy tam giác ABD vuông tại D.
  • hơi dài nha thông cảm

Trong tam giác vuông, góc vuông là góc lớn nhất nên cạnh huyền (đối diện với góc vuông) là cạnh lớn nhất.

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