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Rectangle and its Theorems :On the basis of its properties, there are different theorems.A rectangle is a parallelogram in which each angle is 90

Rectangle and its Theorems :

Statements |
Reasons |

1) ABCD is a rectangle. | 1) Given |

2)∴ ABCD is a Parallelogram. | 2) Every rectangle is a Parallelogram. |

3) AD || BC | 3) By Properties of parallelogram. |

4) ∠A + ∠B = 180^{0} |
4) Interior angles on the same side of transversal are supplementary. |

5) 90 + ∠B = 180 | 5) ∠A = 90 (Given) |

6) ∠B = 90^{0} |
6) By subtraction property. |

7) ∠D= 90 and ∠C= 90 | 7) By properties of parallelogram. |

Statements |
Reasons |

1) ABCD is a rectangle. | 1) Given |

2) AD = BC | 2) Property of rectangle (opposite sides are equal) |

3) AB = AB | 3) Reflexive (common side) |

4) ∠A = ∠B | 4) Each right angle.(property of rectangle) |

5) Δ DAB ≅ Δ CBA | 5) SAS Postulate |

6) AC = BD | 6) CPCTC |

1) The diagonals of a rectangle ABCD meet at ‘O’. If ∠BOC = 44

∠ BOC + ∠BOA = 180 [ Linear pair angles are supplementary]

⇒ 44 + ∠ BOA = 180

⇒ ∠BOA = 180 – 44

⇒ ∠ BOA = 136

As diagonals of a rectangle are equal and bisect each other.

So, OA = OB

⇒ ∠1 = ∠2

∠1 + ∠2 + ∠BOA = 180

2∠1 + 136 = 180

2∠1 = 180 -136

2∠1 = 44

∴ ∠1 = 22

As ∠A = 90

∠A = ∠1 + ∠3

90 = 22 + ∠3

So, ∠3 = 90 – 22

∠3 = 68

So, ∠OAD = 68

• Introduction to Quadrilateral

• Types of Quadrilateral

• Properties of Quadrilateral

• Parallelogram and its Theorems

• Rectangle and its Theorems

• Square and its Theorems

• Rhombus and its Theorems

• Trapezoid (Trapezium)and its Theorems

• Kite and its Theorems

• Mid Point Theorem

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