In this section, we shall discuss some more proofs on basic proportionality.

statements |
Reasons |

1) DE || BC | 1) Given |

2) AD/DB = AE/EC | 2) By Basic Proportionality Theorem |

3) D is the mid point. | 3) Given |

4) AD = DB | 4) By definition of mid point. |

5) AD/DB = 1 | 5) By division property |

6) AE /EC = 1 | 6) From (2) and (5) |

7) AE = EC | 7) By cross multiply |

Statements |
Reasons |

1) FE || AB | 1) Given (in ΔABD) |

2) DE/EB = DF/FA | 2) By Basic proportionality theorem |

3) FE || DC | 3) Given (in ΔCDA) |

4) CE/EA = DF/FA | 4)By Basic proportionality theorem |

5) DE/EB = CE/EA | 5) From (2) and (4) |

Statements |
Reasons |

1) EG || DC | 1) Given (in ΔADC) |

2) AE/ED = AG/GC | 2) By Basic proportionality theorem |

3) GF || AB | 3) Given (in ΔABC) |

4) AG/GC = BF/FC | 4)By Basic proportionality theorem |

5) AE/ED = BF/FC | 5) From (2) and (4) |

• Similarity in Geometry

• Properties of similar triangles

• Basic Proportionality Theorem(Thales theorem)

• Converse of Basic Proportionality Theorem

• Interior Angle Bisector Theorem

• Exterior Angle Bisector Theorem

• Proofs on Basic Proportionality

• Criteria of Similarity of Triangles

• Geometric Mean of Similar Triangles

• Areas of Two Similar Triangles

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