Home
Class 9
MATHS
In Figure, A B C D isa trapezium in whic...

In Figure, `A B C D` isa trapezium in which side `A B` is a parallel to side `D C` and `E` is the mid-point of side `A Ddot` If `F` is a point on the side `B C` such that the segment `E F` is parallel to side `D C` . Prove that `F` is the mid point of `B C` and `E F=1/2(A B+D C)dot`

Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    RD SHARMA ENGLISH|Exercise All Questions|67 Videos
  • RATIONALISATION

    RD SHARMA ENGLISH|Exercise All Questions|130 Videos

Similar Questions

Explore conceptually related problems

In Figure, A B C D isa trapezium in which side A B is a parallel to side D C and E is the mid-point of side A D . If F is a point on the side B C such that the segment E F is parallel to side D C . Prove that F is the mid point of B C and E F=1/2(A B+D C) .

In Figure, line segments A B is parallel to another line segment C DdotO is the mid-point of A Ddot Show that: O is also the mid-point of B D

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

A B C D is a parallelogram and E is the mid-point of B C ,\ D E\ a n d\ A B when produced meet at F . Then A F=

If D is a point on the side A B of /_\ A B C such that A D : D B=3:2 and E is a point on B C such that DE||AC . Find the ratio of areas of /_\ A B C and /_\ B D E .

In Figure, A B C D is a parallelogram and X ,Y are the mid-points of sides A B and D C respectively. Show that A X C Y is a parallelogram.

In Figure, A B C D is a parallelogram. E and F are the mid-points of the sides A B and C D respectively. Prove that the line segments A F and C E triset (divide into three equal parts) the diagonal B Ddot

If D is the mid-point of the side B C of a triangle A B C , prove that vec A B+ vec A C=2 vec A Ddot

In /_\A B C ,D is the mid-point of BC and ED is the bisector of the /_ADB and EF is drawn parallel to B C cutting A C in F . Prove that /_E D F is a right angle.

In Figure, A B C is a triangle in which A B=A Cdot Point D and E are points on the sides AB and AC respectively such that A D=A Edot Show that the points B , C , E and D are concyclic.

RD SHARMA ENGLISH-QUADRILATERALS-All Questions
  1. P ,Q and R are, respectively, the mid-points of sides B C ,C A and A B...

    Text Solution

    |

  2. P is the mid-point of side A B of a parallelogram A B C D . A Line thr...

    Text Solution

    |

  3. In Figure, A B C D isa trapezium in which side A B is a parallel to si...

    Text Solution

    |

  4. In Figure, A B C D is a parallelogram. E and F are the mid-points of t...

    Text Solution

    |

  5. A B C D is a parallelogram. P is a point on A D such that A P=1/3A D a...

    Text Solution

    |

  6. In a triangle A B C ,\ B M\ a n d\ C N are perpendiculars from B\ a...

    Text Solution

    |

  7. In Figure, M ,N and P are the mid-points of A B ,A C and B C respectiv...

    Text Solution

    |

  8. Prove that the line segment joining the mid-points of the diagonals of...

    Text Solution

    |

  9. In a triangle A B C median A D is produced to X such that A D=D Xdot P...

    Text Solution

    |

  10. In Delta ABC the lines are drawn parallel to BC,CA and AB respectively...

    Text Solution

    |

  11. A B C D is a kite having A B=A D and B C=C D . Prove that the figure f...

    Text Solution

    |

  12. Prove that In a parallelogram, opposite side are equal

    Text Solution

    |

  13. The opposite angles of a parallelogram are equal.

    Text Solution

    |

  14. The sides B A and D C of a quadrilateral A B C D are produced as shown...

    Text Solution

    |

  15. In a quadrilateral A B C D ,A O andB O are the bisectors of A/ and /B ...

    Text Solution

    |

  16. The angle of quadrilateral are respectively 100^0,98^0,92^0dot Find th...

    Text Solution

    |

  17. The angles of a quadrilateral are in the ratio 3:5:9: 13. Find all the...

    Text Solution

    |

  18. A diagonal of parallelogram divides it into two congruent triangles.

    Text Solution

    |

  19. In Figure, bisectors of /B and /D of quadrilateral A B C D meet C D...

    Text Solution

    |

  20. In a quadrilateral A B C D ,\ C O\ a n d\ D O are the bisectors of /C\...

    Text Solution

    |