Home
Class 9
MATHS
If AP bisects angle BAC and M is any poi...

If AP bisects angle BAC and M is any point on AP, prove that the perpendiculars drawn from M to AB and AC are equal.

Promotional Banner

Topper's Solved these Questions

  • TRIANGLES

    ICSE|Exercise EXERCISE 9(B)|20 Videos

  • TRIANGLES

    ICSE|Exercise QUESTIONS|8 Videos

  • STATISTICS AND GRAPH WORK

    ICSE|Exercise TOPIC - 2 (4 Marks Questions)|14 Videos

  • TRIGONOMETRICAL RATIOS

    ICSE|Exercise EXERCISE 22(B)|50 Videos

Similar Questions

Explore conceptually related problems

A triangle ABC has angle B = angle C . Prove that : (i) the perpendiculars from the mid-point of BC to AB and AC are equal. (ii) the perpendicular from B and C to the opposite sides are equal.

P is any point in the angle ABC such that the perpendicular drawn from P on AB and BC are equal. Prove that BP bisects angle ABC.

In DeltaABC, angleB= angleC . Prove the perpendiculars from the mid-point of BC to AB and AC are equal.

If DeltaABC is an isosceles triangle with AB = AC. Prove that the perpendiculars from the vertices B and C to their opposite sides are equal.

In the given figures, AB > AC and D is any point on BC. Prove that : AB >AD.

In the figure, BX bisects angle ABC and intersects AC at point D. Line segment CY is perpendicular to AB and intersects BX at point P. If Y is mid-point of AB, prove that : point P is equidistant from A and B.

In the figure, BX bisects angle ABC and intersects AC at point D. Line segment CY is perpendicular to AB and intersects BX at point P. If Y is mid-point of AB, prove that : point D is equidistant from AB and BC.

ABCD is a square. A is joined to a point P on BC and D is joined to a point Q on AB. If AP = DQ, prove that AP and DQ are perpendicular to each other.

In triangle ABC, the sides AB and AC are equal. If P is a point on AB and Q is a point on AC such that AP = AQ, prove that : (i) triangle APC and AQB are congruent. (ii) triangle BPC and CQB are congruent.

In Delta ABC , AB = AC and the bisectors of angles B and C intersect at point O. Prove that : (i) BO = CO (ii) AO bisects angle BAC.

ICSE-TRIANGLES -4 MARKS QUESTIONS
  1. If AP bisects angle BAC and M is any point on AP, prove that the perpe...

    Text Solution

    |

  2. In a triangle ABC, D is mid-point of BC, AD is produced upto E so that...

    Text Solution

    |

  3. In a triangle ABC,D is the mid - point of BC, AD is produced upto E so...

    Text Solution

    |

  4. In a triangle ABC, D is mid-point of BC, AD is produced upto E so that...

    Text Solution

    |

  5. From the given diagram, in which ABCD is a Parallelogram, ABL is a lin...

    Text Solution

    |

  6. From the given diagram, in which ABCD is a Parallelogram, ABL is a lin...

    Text Solution

    |

  7. From the given diagram, in which ABCD is a Parallelogram, ABL is a lin...

    Text Solution

    |

  8. In the given figure, AB = DB and AC = DC. If angleABD=58^(@),angleDBC=...

    Text Solution

    |

  9. In the following figure, AB = AC and AD is perpendicular to BC. BE bis...

    Text Solution

    |

  10. In the following figure, AB = AC and AD is perpendicular to BC. BE bis...

    Text Solution

    |

  11. On the sides AB and AC of triangle ABC, equilateral triangles ABD and ...

    Text Solution

    |

  12. On the sides AB and AC of triangle ABC, equilateral triangles ABD and ...

    Text Solution

    |

  13. In the adjoining figure, OX and RX are the bisectors of the angle Q an...

    Text Solution

    |

  14. In the adjoining figure, OX and RX are the bisectors of the angle Q an...

    Text Solution

    |

  15. In the following figure, OA=OC and AB=BC. Prove that : angleAO...

    Text Solution

    |

  16. In the following figure, OA=OC and AB=BC. Prove that : DeltaAOD...

    Text Solution

    |

  17. In the following figure, OA=OC and AB=BC. Prove that : AD=CD

    Text Solution

    |

  18. The following figure shows a triangle ABC in which AB=AC. M is a point...

    Text Solution

    |

  19. The following figure shows a triangle ABC in which AB=AC. M is a point...

    Text Solution

    |

  20. The following figure shows a triangle ABC in which AB=AC. M is a point...

    Text Solution

    |

  21. The following figure shows a triangle ABC in which AB=AC. M is a point...

    Text Solution

    |