Home
Class 9
MATHS
Diagonals A C and B D of a trapezium A B...

Diagonals `A C` and `B D` of a trapezium `A B C D` with `A B || C D` intersect each other at `O`. Prove that ar `( triangle A O D)=a r( triangle B O C)`.

Promotional Banner

Topper's Solved these Questions

  • ALGEBRAIC IDENTITIES

    RD SHARMA ENGLISH|Exercise All Questions|247 Videos
  • CIRCLE

    RD SHARMA ENGLISH|Exercise All Questions|306 Videos

Similar Questions

Explore conceptually related problems

Diagonals A C\ a n d\ B D of a trapezium A B C D with A B||D C intersect each other at O . Prove that a r\ ( A O D)=\ a r\ ( B O C) .

Diagonals A C and B D of a trapezium A BC D with A B, D C intersect each other at the point O . Using similarity criterion for two triangles, show that (O A)/(O C)=(O B)/(O D) .

In figure, A B C D is a trapezium in which A B||C D . Prove that: a r( triangle A O D)=a r( triangle B O C) .

Diagonal A C\ a n d\ B D of trapezium A B C D , in which A B || D C , intersect each other at Odot The triangle which is equal in area of A O D is A O B (b) B O C (c) D O C (d) A D C

A B C D is a trapezium with A B || D C . A line parallel to A C intersects A B at X and B C at Y . Prove that a r( triangle A D X)=a r(triangle A C Y) .

Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at the point O. Using a similarity criterion for two triangles, show that (O A)/(O C)=(O B)/(O D)

Diagonals A C and B D of a quadrilateral A B C D intersect at O in such a way that a r(triangle A O D)=a r(triangle B O C) . Prove that A B C D is a trapezium.

In Figure, A B C D is a trapezium in which A B||D C .\ \ D C is produced to E such that C E=A B , prove that a r(triangle A B D)=a r (triangle B C E) . Construction: Draw D M\ on B A produced and B N_|_D C

O is any point on the diagonal B D of the parallelogram A B C D . Prove that a r( triangle O A B)=a r(triangle O B C)

In a triangle \ 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 C . Prove that: a r\ (triangle \ L O B)=a r\ (triangle \ M O C)

RD SHARMA ENGLISH-AREA OF PARALLELOGRAMS AND TRIANGLES-All Questions
  1. The diagonals of a parallelogram A B C D intersect at Odot A line thro...

    Text Solution

    |

  2. Show that the segment joining the mid-points of a pair of opposite s...

    Text Solution

    |

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

    Text Solution

    |

  4. In Figure, A B C D is a quadrilateral and B E || A C and also B E meet...

    Text Solution

    |

  5. If a triangle and a parallelogram are on the same base and between the...

    Text Solution

    |

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

    Text Solution

    |

  7. Prove that The area of a parallelogram is the product of its base and...

    Text Solution

    |

  8. Prove that Parallelograms on the same base and between the same para...

    Text Solution

    |

  9. Prove that A diagonal of a parallelogram divides it into two triangl...

    Text Solution

    |

  10. If each diagonal of a quadrilateral separates it into two triangles...

    Text Solution

    |

  11. The area of a triangle is half the product of any of its sides and t...

    Text Solution

    |

  12. Triangles A B C and DBC are on the same base B C with A, D on opposite...

    Text Solution

    |

  13. If the diagonals A C ,B D of a quadrilateral A B C D , intersect at O ...

    Text Solution

    |

  14. If P is any point in the interior of a parallelogram A B C D , then pr...

    Text Solution

    |

  15. The diagonals of quadrilateral A B C D ,A C and B D intersect in Odot ...

    Text Solution

    |

  16. X Y is a line parallel to side B C of triangle A B C. BE ll AC and C...

    Text Solution

    |

  17. In Figure, A B C D is a trapezium in which A B D C and D C=40c m and ...

    Text Solution

    |

  18. Show that the diagonals of a parallelogram divide it into four tria...

    Text Solution

    |

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

    Text Solution

    |

  20. A B C D is a parallelogram whose diagonals A C and B D intersect at Od...

    Text Solution

    |