Home
Class 9
MATHS
D is the mid-point of side B C of \ A...

`D` is the mid-point of side `B C` of `\ A B C\ a n d\ E` is the mid-point of `B Ddot` If `O` is the mid-point of `A E ,` prove that `a r\ (\ B O E)=1/8a r\ (\ A B C)`

Text Solution

Verified by Experts

Given: D is the midpoint of side BC of ∆ABC. E is the midpoint of BD and O is the midpoint of AE.
Since AD and AE are the medians of `triangleABC` and `triangleABD` respectively.
`therefore` ar(`triangleABD`)=`1/2`ar(`triangleABC)`_____1
ar(`triangleABE`)=`1/2`ar(`triangleABD`)____2
OB is a median of `triangleABE`
`therefore` ar(`triangleBOE`)=`1/2`ar(`triangleABE`)____3
From 1,2 and 3
ar(`triangleBOE`)=`1/8`ar(`triangleABC`) hence proved
Promotional Banner

Topper's Solved these Questions

  • ALGEBRAIC IDENTITIES

    RD SHARMA|Exercise All Questions|247 Videos

  • CIRCLE

    RD SHARMA|Exercise All Questions|306 Videos

Similar Questions

Explore conceptually related problems

D is the mid-point of side B C of A B C and E is the mid-point of B Ddot If O is the mid-point of A E , prove that a r( B O E)=1/8a r( A B C)

In A A B C ,\ P\ a n d\ Q are respectively the mid-points of A B\ a n d\ B C and R is the mid-point of A Pdot Prove that: a r\ ( R Q C)=3/8\ a r\ (\ A B C)

In A A B C ,\ P\ a n d\ Q are respectively the mid-points of A B\ a n d\ B C and R is the mid-point of A Pdot Prove that: a r\ (\ P R Q)=1/2a r\ (\ A R C)

D is the mid-point of side BC of Delta ABC and E is the mid-point of BO. If O is the mid-point of AE, then ar( Delta BOE) = 1/k ar( Delta ABC). Then k equals

In A A B C ,\ P\ a n d\ Q are respectively the mid-points of A B\ a n d\ B C and R is the mid-point of A Pdot Prove that: a r\ ( P B Q)=\ a r\ (\ A R C)

D is the mid-point of side AB of the triangle ABC.E is the mid-point of CD and F is the mid-point of AE. Prove that 8 xx " area of " (DeltaAFD) = " area of " Delta ABC

In a \ A B C , If L\ a n d\ M are points on A B\ a n d\ A C respectively such that L M B Cdot Prove that: a r\ (\ L O B)=a r\ (\ M O C)

If A D is a median of a triangle A B C ,\ then prove that triangles A D B\ a n d\ A D C are equal in area. If G is the mid-point of median A D , prove that a r\ ( B G C)=2a r\ (\ A G C)

A B C is a triangle in which D is the mid-point of B C and E is the mid-point of A Ddot Prove that area of B E D=1/4a r e aof A B Cdot GIVEN : A A B C ,D is the mid-point of B C and E is the mid-point of the median A Ddot TO PROVE : a r( B E D)=1/4a r( A B C)dot

In Figure, A B C\ a n d\ B D E are two equilateral triangls such that D is the mid-point of B CdotA E intersects B C in Fdot Prove that: a r\ (\ F E D)=1/8a r\ (\ A F C)

RD SHARMA-AREA OF PARALLELOGRAMS AND TRIANGLES-All Questions
  1. In Figure, ABC and BDE are two equilateral triangles such that D is th...

    Text Solution

    |

  2. In Figure, A B C\ a n d\ B D E are two equilateral triangls such tha...

    Text Solution

    |

  3. D is the mid-point of side B C of \ A B C\ a n d\ E is the mid-p...

    Text Solution

    |

  4. In Figure, X and Y are the mid-points of AC and A B respectively, QP...

    Text Solution

    |

  5. In Figure ABCD and AEFD are two parallelograms. Prove that: PE=FQ

    Text Solution

    |

  6. In Figure, ABCD and AEFD are two parallelograms? Prove that: ar (APE):...

    Text Solution

    |

  7. In Figure, ABCD is a parallelogram O s any point on AC, PQ "parallel" ...

    Text Solution

    |

  8. In a ABC , If L and M are points on AB and AC respectively such that L...

    Text Solution

    |

  9. In a ABC , If L and M are points on AB and AC respectively such that L...

    Text Solution

    |

  10. In a ABC , If L and M are points AB and AC respectively such that L...

    Text Solution

    |

  11. In a ABC , If L and M are points on AB and A C respectively such that ...

    Text Solution

    |

  12. In Figure D and E are two points on BC such that BD=DE=EC Show that ar...

    Text Solution

    |

  13. In Figure, A B C is a right triangle right angled at A ,\ B C E D ,\...

    Text Solution

    |

  14. In Figure, A B C is a right triangle right angled at A ,\ B C E D ,\...

    Text Solution

    |

  15. In Figure, A B C is a right triangle right angled at A ,\ B C E D ,\...

    Text Solution

    |

  16. In Figure, A B C is a right triangle right angled at A ,\ B C E D ,\...

    Text Solution

    |

  17. In Figure, A B C is a right triangle right angled at A ,\ B C E D ,\...

    Text Solution

    |

  18. In Figure, A B C is a right triangle right angled at A ,\ B C E D ,\...

    Text Solution

    |

  19. In Fig.9.33, ABC and BDE are two equilateral triangles such that D is ...

    Text Solution

    |

  20. In Figure, ABCD is a rectangle in which CD=6 cm ,AD=8 cm Find the area...

    Text Solution

    |