Home
Class 10
MATHS
AD is the height of the triangle ABC. I...

AD is the height of the triangle ABC. If `AB gt AC`,then prove that `AB^(2) -AC^(2)= BD^(2) -CD^(2)`.

Promotional Banner

Topper's Solved these Questions

  • PYTHAGORAS THEOREM

    CALCUTTA BOOK HOUSE|Exercise EXAMPLE 6|4 Videos

  • PYTHAGORAS THEOREM

    CALCUTTA BOOK HOUSE|Exercise EXAMPLE 3|4 Videos

  • PROBLEMS RELATED TO DIFFERENT SOLIDS AND OBJECTS

    CALCUTTA BOOK HOUSE|Exercise Long - answer type questions (LA):|20 Videos

  • QUADRATIC EQUATION IN ONE VARIABLE

    CALCUTTA BOOK HOUSE|Exercise EXERCISE-1.5|40 Videos

Similar Questions

Explore conceptually related problems

If in DeltaABC, AD_|_ BC, then prove that AB^(2) + CD^(2) = AC^(2) + BD^(2)

In Delta ABC, AD_|_ BC . Prove that AB^(2) - BD^(2) =AC^(2) -CD^(2)

In Delta ABC , AD_|_ BC which intersects BC at D. If BD =3 CD , then prove that 2AB^(2) = 2AC^(2)+BC^(2)

In Delta ABC,/_A = right angle. If CD is a median, then prove that BC^(2) = CD^(2)+ 3AD^(2) .

ABC is a right-angled isoscels triangles of which /_C is a right angle. If D is any point on AB. Then prove that AD^(2) + BD^(2) = 2CD^(2)

Delta ABC is an obtus triangle in which /_B = obtus angle. If AD is perpendicular to BC ( or extended BC ) ,then prove that AC^(2) = AB^(2) +BC^(2) + 2BC xx BD .

ABC is an equilateral triangle. AD is perpendicular to BC. Prove that AB^(2) + BC^(2) + CA^(2) =4AD^(2)

ABC is an isosceles triangle right angled at C. Prove that AB^(2) = 2AC^(2) .

ABCD is a cyclic quadrilateral. If AB = DC, then prove that AC= BD.

CALCUTTA BOOK HOUSE-PYTHAGORAS THEOREM -LONG-ANSWER TYPE QUESTION
  1. ABC is a right-angled triangle of which /A = right angle. P and Q are...

    Text Solution

    |

  2. If the diagonals of the quadrilateral ABCD intersect each other orthog...

    Text Solution

    |

  3. AD is the height of the triangle ABC. If AB gt AC,then prove that AB^...

    Text Solution

    |

  4. Two perpendicular BD and CE are drawn from the vertices B and C respe...

    Text Solution

    |

  5. ABC is a right-angled isoscels triangles of which /C is a right angle...

    Text Solution

    |

  6. In Delta ABC,/A = right angle. If CD is a median, then prove that BC^(...

    Text Solution

    |

  7. OX,OY and OZ are the perpendiculars drawn from an internal point O of ...

    Text Solution

    |

  8. In the Delta RST, /S right angle.X and Y are the midpoints of RS and ...

    Text Solution

    |

  9. If in DeltaABC, AD| BC,then prove that AB^(2) + CD^(2) = AC^(2) + BD^...

    Text Solution

    |

  10. Prove that the area of the square drawn on the diagonal of a square is...

    Text Solution

    |

  11. O is any point inside a rectangle ABCD, Prove that OA^(2) + OC^(2)= OB...

    Text Solution

    |

  12. ABCD is a rhombus.Prove that AB^(2) + BC^(2) +CD^(2) + DA^(2) = AC^(2)...

    Text Solution

    |

  13. In Delta ABC, AD| BC . Prove thatAB^(2) - BD^(2) =AC^(2) -CD^(2)

    Text Solution

    |

  14. In Delta ABC , AD| BC which intersects BC at D. If BD =3 CD, then pro...

    Text Solution

    |

  15. In the isosceles triangle ABC, AB=AC and BE is perpendicular to AC fro...

    Text Solution

    |

  16. In an isosceles right-angled triangle ABC,/B=90^(@). The bisector of /...

    Text Solution

    |

  17. Prove that the sum of the areas of the squares drawn on the sides of a...

    Text Solution

    |

  18. Delta PQR is a right-angled isosceles triangle of which the two sides...

    Text Solution

    |

  19. P is an external point of the square ABCD. If PA gt PB ,then prove tha...

    Text Solution

    |

  20. In the right-angled ABC, /A =1 right angle. BE and CF are two medians...

    Text Solution

    |