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Mathematics Dictionary
Dr. K. G. Shih
Figure 066 : Pythagorean Law

  • Q01 | - Diagram : Prove Pythagorean Law
  • Q02 | - Prove area BXYQ = area ABHK
  • Q03 | - Prove area CXYF = area AMNC
  • Q04 | - Reference

Q01. Diagram : How to prove ?



Hove to prove ?
  • 1. Prove area BXYQ = area ABHK
  • 2. Prove area CXYF = area AMNC
  • 3. Then Area ABCD = area ABHK + area AMNC

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Q02. Diagram : Prove area BXYQ = area ABHK


Prove area BXYQ = area ABHK
  • Area of triangle HBC = (area ABHK)/2
  • Area of triangle ABQ = (area BXYQ)/2
  • Triangle HBC is congruent to triangle ABQ
    • AB = HB
    • BC = BQ
    • Angle HBC = angle ABQ
    • Hence SAS condition is satisfied

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Q03. Reference




Prove area AMNC = area CXYP
  • Area of triangle BCN = (area AMNC)/2
  • Area of triangle ACP = (area CXYP)/2
  • Triangle BCN is congruent to triangle ACP
    • AC = CN
    • BC = CP
    • Angle BCN = angle ACP
    • Hence SAS condition is satisfied

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Q04. Reference
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