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Proof On Pythagorean Theorem

Statements |
Reasons |

1) ∠ABC = 90^{0} |
1) Given |

2) BD ⊥ AC | 2) By construction |

3) ∠ADB = 90^{0} |
3) By definition of perpendicular |

4) ∠ADB = ∠ABC | 4) Each of 9090^{0} |

5) ∠A = ∠A | 5) Reflexive |

6) ΔADB ~ ΔABC | 6) By AA postulate |

7) AD/AB = AB/AC | 7) By basic proportionality theorem |

8) AB^{2} = AD x AC |
8) By cross multiplication |

9) ∠CDB = ∠ABC | 9) Each 90^{0} |

10) ∠C = ∠C | 10) Reflexive |

11) ΔBDC ~ ΔABC | 11) By AA postulate |

12) DC/BC = BC/AC | 12) By basic proportionality theorem |

13) BC^{2} = DC x AC |
13) By cross multiplication |

14) AB^{2} + BC^{2} = AD x AC + AC x DC |
14) By adding (8) and (13) |

15) AB^{2} + BC^{2} = AC(AD + DC) |
15) By distributive property |

16) AB^{2} + BC^{2}= AC^{2} |
16) As AC = AD + DC and by substitution |

Application based on Proof On Pythagorean Theorem.

In ΔADB,

AB

In ΔADC,

AC

AC

AC

AC

AC

AB

AC

• Introduction of Pythagorean Theorem

• Converse of Pythagorean Theorem

• Pythagorean Triples

• Application On Pythagorean Theorem

• Proof on Pythagorean Theorem

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