Home
Class 9
MATHS
In parallelogram ABCD, the bisector of a...

In parallelogram ABCD, the bisector of angle A meets DC at P and AB= 2AD. Prove that:
Angle APB= `90^(@)`

Promotional Banner

Topper's Solved these Questions

  • RECTILINEAR FIGURES

    ICSE|Exercise POLYGONS - 3 MARKS QUESTIONS|5 Videos

  • RECTILINEAR FIGURES

    ICSE|Exercise POLYGONS - 4 MARKS QUESTIONS|4 Videos

  • RECTILINEAR FIGURES

    ICSE|Exercise Exercise 14(B)|16 Videos

  • RATIONAL AND IRRATIONAL NUMBERS

    ICSE|Exercise EXERCISE 1 (D)|21 Videos

  • SIMULTANEOUS EQUATIONS

    ICSE|Exercise EXERCISE 6 (G)|13 Videos

Similar Questions

Explore conceptually related problems

In parallelogram ABCD, the bisector of angle A meets DC at P and AB= 2AD. Prove that: BP bisects angle B

In parallelogram ABCD, the bisector of angle A meets DC at P and AB = 2AD. Prove that : (i) BP bisects angle B. (ii) Angle APB = 90^(@)

In a parallelogram ABCD, the bisector of angleA bisects the line B at point X. Prove that AD = 2AB.

In a parallelogram ABCD, the bisectors of angleA and angleB intersect each other at point P. Prove that angleAPB=90^(@).

In a parallelogram ABCD, AB= 20 cm and AD= 12cm. The bisector of angle A meets DC at E and BC produced at F. Find the length of CF.

In parallelogram ABCD, the bisectors of adjacent angles A and D intersect each other at point P. prove that angleAPD=90^(@) .

In a tringle ABC, AB = AC and bisector of angle A meets BC at D. Prove that : (i) DeltaABD cong DeltaACD (ii) AD is perpendicular to BC.

In parallelogram ABCD, E is the mid-point of side AB and CE bisect angle BCD. Prove that : (i) AE=AD (ii) DE bisect angleADC and (iii) Angle DEC is a right angle.

In the following figure , ABCD is a cyclic quadrilateral in which AD is parallel to BC . If the bisector of angle A meets BC at point E and given circle at point F, prove that : (i) EF =FC (ii) BF = DF

ABCD is a parallelogram in which angleDAB=80^(@) . Bisector of angleA and angleB meets CD at P. Prove that : (i) AD = DP (ii) CP = CB (iii) DC = 2AD

ICSE-RECTILINEAR FIGURES-Exercise 14(C )
  1. In the given figure, ABCD is a parallelogram. Prove that: AB= 2BC

    Text Solution

    |

  2. Prove that the bisectors of opposite angles of a parallelogram are par...

    Text Solution

    |

  3. The bisectors of the angle of a parallelogram enclose a parallelogr...

    Text Solution

    |

  4. Prove that the bisectors of the interior angles of a rectangle form a ...

    Text Solution

    |

  5. In parallelogram ABCD, the bisector of angle A meets DC at P and AB= 2...

    Text Solution

    |

  6. In parallelogram ABCD, the bisector of angle A meets DC at P and AB= 2...

    Text Solution

    |

  7. Points M and N are taken on the diagonal AC of a parallelogram ABCD su...

    Text Solution

    |

  8. In the following figure, ABCD is a parallelogram. Prove that: AP...

    Text Solution

    |

  9. In the following figure, ABCD is a parallelogram. Prove that: BP ...

    Text Solution

    |

  10. In the following figure, ABCD is a parallelogram. Prove that: ang...

    Text Solution

    |

  11. ABCD is a square. A is joined to a point P on BC and D is joined to a ...

    Text Solution

    |

  12. In a quadrilateral ABCD, AB= AD and CB= CD. Prove that: AC bisects ...

    Text Solution

    |

  13. In a quadrilateral ABCD, AB= AD and CB= CD. Prove that: AC is perpe...

    Text Solution

    |

  14. The following figure shows a trapezium ABCD in which AB is parallel to...

    Text Solution

    |

  15. The following figure shows a trapezium ABCD in which AB is parallel to...

    Text Solution

    |

  16. The following figure shows a trapezium ABCD in which AB is parallel to...

    Text Solution

    |

  17. In a parallelogram, prove that the bisectors of any two consecutive an...

    Text Solution

    |

  18. Prove that the bisectors of opposite angles of a parallelogram are par...

    Text Solution

    |

  19. The diagonals of a rectangle intersect each other at right angles. Pro...

    Text Solution

    |

  20. In the following figure, ABCD and PQRS are two parallelogram such that...

    Text Solution

    |