Statements |
Reasons |

1) ∠ADC = ∠ACB | 1) Each 90^{0} and by construction |

2) ∠A = ∠A | 2) Reflexive (common) |

3) ΔADC ~ ΔABC | 3) AA similarity |

4) AD / AC = AC / AB | 4) If two triangles are similar then corresponding sides are proportional |

5) AC^{2} = AD x AB |
5) Cross multiplication |

6) ∠BDC = ∠ACB | 6) Each 90^{0} and by construction |

7) ∠B = ∠B | 7) Reflexive (common) |

8) ΔCDB = ΔABC | 8) AA similarity |

9)BD / BC = BC / AB | If two triangles are similar then corresponding sides are proportional |

10) BC^{2} = BD x AB |
10) Cross multiplication |

11) AC^{2} + BC^{2} =AD x AB + BD x AB |
11) Add (5) and (10) |

12) AC^{2} + BC^{2} = AB ( AD + BD ) |
12) Taking AB as common |

13) AC^{2} + BC^{2} = AB x AB |
13) Substitution ( AD + BD = AB) |

14) AC^{2} + BC^{2} = AB^{2} |
14) Simplify |

15) c^{2} = a^{2} + b^{2} |
15) From the diagram. Hence proved. |

If the square of hypotenuse is equal to the sum of squares of other two sides then it is a right angled triangle.

If c

•

• GeometryProof-1

• GeometryProof 2

• area-similartriangles

• geometry pythagorean theorem

GMAT

GRE

1st Grade

2nd Grade

3rd Grade

4th Grade

5th Grade

6th Grade

7th grade math

8th grade math

9th grade math

10th grade math

11th grade math

12th grade math

Precalculus

Worksheets

Chapter wise Test

MCQ's

Math Dictionary

Graph Dictionary

Multiplicative tables

Math Teasers

NTSE

Chinese Numbers

CBSE Sample Papers