Home
Class 10
MATHS
In Fig.6.60, AD is a median of a tria...

In Fig.6.60,
AD is a median of a triangle ABC and `AM_|_BC`.Prove that :(iii)`AC^2+AB^2=2AD^2+1/2BC^2`

Promotional Banner

Topper's Solved these Questions

  • TRIANGLES

    R G PUBLICATION|Exercise EXERCISE|108 Videos

  • SURFACE AREA AND VOLUMES

    R G PUBLICATION|Exercise EXERCISE|69 Videos

Similar Questions

Explore conceptually related problems

In Fig.6.60, AD is a median of a triangle ABC and AM_|_BC .Prove that :(ii) AB^2=AD^2-BC.DM+((BC)/2)^2

In Fig.6.60, AD is a median of a triangle ABC and AM_|_BC .Prove that :(i) AC^2=AD^2+BC.DM+((BC)/2)^2

In Fig.6.53,ABD is a triangle right angle at A and AC_|_BD .Show that (ii) AC^2=BC.DC .

In Fig.6.59, ABC is a triangle in which angleABC<90^@ and AD_|_BC .Prove that AC^2=AB^2+BC^2-2BC.BD .

In Fig.6.53,ABD is a triangle right angle at A and AC_|_BD .Show that (iii) AD^2=BD.CD .

In Fig.6.58, ABC is a triangle in which angleABC>90^@ and AD_|_CB produced.Prove that AC^2=AB^2+BC^2+2BC.BD .

In Fig.6.53,ABD is a triangle right angle at A and AC_|_BD .Show that (i) AB^2=BC.BD .

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

Fig.6.45,O is a point in the interior of a triangle ABC, OD_|_BC,OE_|_AC and OF_|_AB .Show that (ii) AF^2+BD^2+CE^2=AE^2+CD^2+BF^2

If PB and AQ are the medians of a ∆ABC right angled at C. Prove that 4AQ^2 = 4 AC^2 + BC^2

R G PUBLICATION-TRIANGLES-EXERCISE
  1. In Fig.6.60, AD is a median of a triangle ABC and AM|BC.Prove that :(i...

    Text Solution

    |

  2. In Fig.6.60, AD is a median of a triangle ABC and AM|BC.Prove that :(i...

    Text Solution

    |

  3. In Fig.6.60, AD is a median of a triangle ABC and AM|BC.Prove that ...

    Text Solution

    |

  4. In Fig.6.61, two chords AB and CD intersect each other at the point P....

    Text Solution

    |

  5. In Fig.6.61, two chords AB and CD intersect each other at the point P....

    Text Solution

    |

  6. In Fig.6.62, two chords AB and CD of a circle intersect each other at ...

    Text Solution

    |

  7. In Fig.6.62, two chords AB and CD of a circle intersect each other at ...

    Text Solution

    |

  8. State basic proportionality theorem.

    Text Solution

    |

  9. In the adjoining figure, DE||BC and AD=1 cm,BD=2 cm.What is the ratio...

    Text Solution

    |

  10. The areas of two similar triangles are 169cm^2 and 121cm^2respectively...

    Text Solution

    |

  11. If triangle ABC and triangleDEFare similar triangle such thatangleA=57...

    Text Solution

    |

  12. If the altitude of two similar triangle are in the ratio 2:3 what is t...

    Text Solution

    |

  13. State Pythagoras theorem.

    Text Solution

    |

  14. The lengths of the diagonals of a rhombus are 30cm and 40cm.Find the s...

    Text Solution

    |

  15. In an isosceles triangleABCif AC=BC and AB^2=2AC^2 then what is the me...

    Text Solution

    |

  16. What is the height of an equilateral triangle having each side 12 cm?

    Text Solution

    |

  17. Sides of two similar triangle are in the ratio 4:9.Areas of these tria...

    Text Solution

    |

  18. triangleABC~triangleDEFsuch that ar(triangleABC) =36cm^2and(triangleDE...

    Text Solution

    |

  19. triangleABC and triangleDEFare two equilateral triangle such that D is...

    Text Solution

    |

  20. Two isosceles triangles have their corresponding angles equal and thei...

    Text Solution

    |