If the two lines are parallel then their intercepts are in proportion.

3) If DE || AQ and DE || AR. Prove that EF || QR.

Given : DE || OQ and DF || OR

Prove that : EF || QR.

Proof :

Statements |
Reasons |

1) DE || OQ | 1) Given (ΔPOQ) |

3) PE/EQ = PD/DO | 3) Basic Proportionality Theorem |

4) DF || OR | 4) Given (ΔPOR) |

5) PF/FR = PD/DO | 5)Basic Proportionality Theorem |

6) PE/EQ = PD/DO | 6) From (2) and (4) (Transitivity) |

7) EF || QR | 7) Converse of Basic Proportionality Theorem |

4) Given : A, B and C are the points on OP,OQ and OR respectively such that AB || PQ and AC || PR.

Given: AB || PQ and AC || PR.

Prove that : BC || QR

Proof :

Statements |
Reasons |

1) AB || PQ | 1) Given (ΔOPQ) |

3) OA/AP = OB/BQ | 3) Basic Proportionality Theorem |

4) AC || PR | 4) Given (ΔOPR) |

5) OA/AP = OC/CR | 5)Basic Proportionality Theorem |

6) OB/BQ = OC/CR | 6) From (2) and (4) (Transitivity) |

7) BC || QR | 7) Converse of Basic Proportionality Theorem |

5) In given figure, DE || BC and CD || EF. Prove that AD

Given : DE || BC and CD || EF

Prove that : AD

Proof :

Statements |
Reasons |

1) DE || BC | 1) Given (ΔABC) |

3) AB/AD = AC/AE | 3) Basic Proportionality Theorem |

4) FE || DC | 4) Given (ΔADC) |

5) AD/AF = AC/AE | 5)Basic Proportionality Theorem |

6) AB/AD = AD/AF | 6) From (2) and (4) (Transitivity) |

7) AD^{2} = AB x AF |
7) Cross multiply |

•

• GeometryProof-1

• GeometryProof 2

• Proofs on Area of similar triangles

• Pythagorean theorem

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