Home
Class 12
MATHS
Prove using vectors: If two medians of a...

Prove using vectors: If two medians of a triangle are equal, then it is isosceles.

Text Solution

Verified by Experts

`BE=CD`. Given

`DX=EY` proved

`ΔCDX~=ΔBEY` following RHS rule.

So

`/_EBY=/_DCX or /_EBC=/_DCB`

Now in `DCB` and` EBC` we have

`BE=CD. ` given

`BC ` common

...
Promotional Banner

Topper's Solved these Questions

  • RELATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|197 Videos

  • SCALAR TRIPLE PRODUCT

    RD SHARMA|Exercise Solved Examples And Exercises|59 Videos

Similar Questions

Explore conceptually related problems

Prove using vectors: Medians of a triangle are concurrent.

If the medians of a triangle are equal,then the triangle is

Prove that the medians of an equilateral triangle are equal.

The median of a triangle divides it into two

Prove that sum of any two medians of a triangle is greater than the third median.

Prove using vectors: The median to the base of an isosceles triangle is perpendicular to the base.

Prove that the sum of three vectors determined by the medians of a triangle directed from the vertices is zero.

If the median to the base of a triangle is perpendicular to the base,then triangle is isosceles.

If the median to the base of a triangle is perpendicular to the base then triangle is isosceles.

RD SHARMA-SCALAR OR DOT PRODUCT-Solved Examples And Exercises
  1. Show that the vectors vec a=3 hat i-2 hat j+ hat k , vec b=3 hat j+5 ...

    Text Solution

    |

  2. (Projection Formulae) if a ,b ,c are the lengths of the sides opposite...

    Text Solution

    |

  3. Prove using vectors: If two medians of a triangle are equal, then it i...

    Text Solution

    |

  4. Find the angle between two vectors vec a and vec b with magnit...

    Text Solution

    |

  5. Find the angle between the vectors 5hat i+3 hat j+4 hat k and 6 hat i...

    Text Solution

    |

  6. Find the projection of the vector 7 hat i+ hat j-4 hat k in vec a=2 ha...

    Text Solution

    |

  7. For any vector vec r , prove that vec r=( vec rdot hat i) hat i+( ve...

    Text Solution

    |

  8. Find veca * vec b when vec a=2 hat i+2 hat j- hat ka n d vec b=6...

    Text Solution

    |

  9. Find the value of lambda so that the vectors vec a=2 hat i+lambda hat...

    Text Solution

    |

  10. Find the value of p for which the vectors vec a=3 hat i+2 hat j+9 ha...

    Text Solution

    |

  11. Find the values of a which the vector vec r=(a^2-4) hat i+2 hat j-(a^...

    Text Solution

    |

  12. If vec a , vec b , vec c are unit vector, prove that | vec a- vec b|...

    Text Solution

    |

  13. If vec a , vec b , vec c are mutually perpendicular unit vectors, fin...

    Text Solution

    |

  14. Find the value of c for which the vectors vec a=(clog2x) hat i-6 hat...

    Text Solution

    |

  15. Let vec a= hat i+4 hat j+2 hat k ,\ \ vec b=3 hat i-\ 2 hat j+7 hat ...

    Text Solution

    |

  16. Dot products of a vector with vectors 3 hat i-5 hat k ,2 hat i+7 hat j...

    Text Solution

    |

  17. Let vec a , vec b , vec c be three vectors such that | vec a|=1,| vec...

    Text Solution

    |

  18. (Cosine Formulae) if a ,b ,c are the lengths of the sides opposite res...

    Text Solution

    |

  19. Prove that the altitudes of a triangle are concurrent.

    Text Solution

    |

  20. Find the components of a unit vector which is perpendicular to the v...

    Text Solution

    |