Home
Class 9
MATHS
A D is one of the medians of a A B Cd...

`A D` is one of the medians of a ` A B Cdot. X` is any point on `AD` . Show that `ar( ABX)=ar ( A C X)`

Text Solution

Verified by Experts

Solution:
`/_\ ABC`,
`AD` is median,
`ar(/_\ABD)=ar(/_\ADC)......(1)`
`/_\XBC,`
`XD` is median,
`ar(XBD) = ar(XDC)......(2)`
Substract eq `(2)` from `(1)`
`ar(/_\ABD) -ar(/_\XBD) = ar(/_\ADC) - ar(/_\ XDC)`
`ar(/_\ABX)=ar(/_\ACX)`
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

In the adjoining figure, AD is the median of Delta ABC and X be any point on side AD. Prove that: area (Delta ABX) = " area " (Delta ACX)

In a ABC,E is the mid-point of median AD Show that ar(BED)=(1)/(4) ar (ABC)

In Fig.9.23,E is any point on median AD of a Delta ABC Show that ar (ABE)=ar(ACE)

In a triangle ABC,E is the mid-point of median AD.Show that quad ar(BED)=(1)/(4)ar(ABC)

In the figure, E is any point on median AD of a triangleABC . Show that ar( triangleABE )= ar( triangleACE ).

In a triangle ABC, E is the mid-point of median AD. Show that ar (triangleBED)=1/4 ar( triangleABC ).

In Fig.9.17, PQRS and ABRS are parallelograms and X is any point on side BR. Show that (i) ar(PQRS)=ar(ABRS) (ii) ar (AXS)backslash=(1)/(2)ar(PQRS)

ABC is a triangle in which D is the midpoint of BC and E is the midpoint of AD. Prove that ar(triangleBED)=(1)/(4)ar(triangleABC) .

In Fig.30D and E are to points on BC such that BD=DE=EC. Show that ar(ABD)=ar(ADE)=ar(AEC)

RD SHARMA-AREA OF PARALLELOGRAMS AND TRIANGLES-All Questions
  1. If A B C D is a parallelogram, then prove that ar (triangle A B D)= ...

    Text Solution

    |

  2. Show that a median of a triangle divides it into two triangles of eq...

    Text Solution

    |

  3. A D is one of the medians of a A B Cdot. X is any point on AD . S...

    Text Solution

    |

  4. In a A B C ,E is the mid-point of median A Ddot Show that ar ( B E ...

    Text Solution

    |

  5. In Figure, A B C D is a quadrilateral and B E|A C and also B E meets...

    Text Solution

    |

  6. Diagonals A C and B D of a trapezium A B C D with A B||D C intersect...

    Text Solution

    |

  7. In Figure, A B C D E\ is a pentagon. A line through B parallel to A...

    Text Solution

    |

  8. Show that the diagonals of a parallelogram divide it into four trian...

    Text Solution

    |

  9. The diagonals of quadrilateral A B C D ,AC and B D intersect in O...

    Text Solution

    |

  10. If the diagonals A C ,\ B D of a quadrilateral A B C D , intersect...

    Text Solution

    |

  11. If each diagonals of a quadrilateral separates it into two triangles...

    Text Solution

    |

  12. Show that the area of a rhombus is half the product of the lengths o...

    Text Solution

    |

  13. The side AB of a parallelogram ABCD is produced to any point P. A line...

    Text Solution

    |

  14. A villager Itwari has a plot of land of the shape of a quadrilateral...

    Text Solution

    |

  15. A B C D is a trapezium with A B|\|D C . A line parallel to A C int...

    Text Solution

    |

  16. Diagonals A C\ a n d\ B D of a quadrilateral A B C D intersect a...

    Text Solution

    |

  17. In Figure, A P B Q\ C Rdot Prove that a r\ ( A Q C)=\ a r\ (P B R)

    Text Solution

    |

  18. In Fig.9.29, a r\ (B D P)\ =\ a r\ (A R C)and a r\ (B D P)\ =\ a r\ (A...

    Text Solution

    |

  19. Diagonals A C and B D of a quadrilateral A B C D intersect at O in suc...

    Text Solution

    |

  20. In Fig. 9.25, diagonals AC and BD of quadrilateral ABCD intersect at O...

    Text Solution

    |