Home
Class 9
MATHS
In a parallelogram A B C D ,E ,F are any...

In a parallelogram `A B C D ,E ,F` are any two points on the sides `A B` and `B C` respectively. Show that `a r( A D F)=a r( D C E)dot`

Text Solution

Verified by Experts

`In/_DCE` and parallelogram ABCD
have same base between same
`ar(/_DCE)=1/2ar(ABCD)-(1)`
`In /_AOF` and parallelogram ABCD
have same base AD and between same lines
`ar(/_ADF)=1/2ar(ABCD)-(2)`
`ar(/_DCE)=ar(/_ADF)`.
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

Show that the segment joining the mid-points of a pair of opposite sides of a parallelogram, divides it into two equal parallelograms. GIVEN : A parallelogram A B C DdotE and F are the mid-points of opposite sides A B and C D respectively. TO PROVE : a r(^(gm)A E F D)=a r(^(gm)E B C F) CONSTRCUTION : Join E Fdot

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

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. Figure

p A N D q are any two points lying on the sides D C a n d A D respectively of a parallelogram A B C Ddot Show that a r( A P B)=a r ( B Q C)dot

X Y isa line parallel to side B C of A B CdotB E A and C F A B meet X Y in E and F respectively.Show that a r( A B E)=a r( A C F)dot

A B C D is a parallelogram and E\ a n d\ F are the centroids of triangles A B D\ a n d\ B C D respectively, then E F= (a) A E (b) B E (c) C E (d) D E

In a A B C ,\ D ,\ E ,\ F are the mi-points of sides B C ,\ C A\ a n d\ A B respectively. If a r( A B C)=16 c m^2, then a r\ (t r a p e z i u m\ F B C E)= 4\ c m^2 (b) 8\ c m^2 (c) 12 c m^2 (d) 10 c m^2

Let A B C be an isosceles triangle in which A B=A Cdot If D ,\ E ,\ F be the mid-points of the sides B C ,\ C A\ a n d\ A B respectively, show that the segemtn A D\ a n d\ E F bisect each other at right angles.

A point D is taken on the side B C of a A B C such that B D=2d Cdot Prove that a r( A B D)=2a r( A D C)dot

In Figure D\ a n d\ E are two points on B C such that B D=D E=E Cdot Show that a r(\ A B D)=\ a r\ (\ A D E)=a r\ (\ A E C)dot

RD SHARMA-AREA OF PARALLELOGRAMS AND TRIANGLES-All Questions
  1. Any point D is taken in the base B C of a triangle A B C\ a n d\...

    Text Solution

    |

  2. In A B C ,D is the mid-point of A B ,P is any point of B CdotC Q P D...

    Text Solution

    |

  3. In a parallelogram A B C D ,E ,F are any two points on the sides A B a...

    Text Solution

    |

  4. In Figure, A B C D is a trapezium in which A B||D C ,\ \ D C is prod...

    Text Solution

    |

  5. Prove that the area of an equilateral triangle is equal to (sqrt(3)...

    Text Solution

    |

  6. A B C D is a trapezium with A B D Cdot A line parallel to A C interse...

    Text Solution

    |

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

    Text Solution

    |

  8. A B C is a triangle in which D is the mid-point of B C and E is the mi...

    Text Solution

    |

  9. A B C D is a parallelogram X and Y are the mid-points of B C and C D r...

    Text Solution

    |

  10. The diagonals of a parallelogram A B C D intersect at a point Od...

    Text Solution

    |

  11. The medians B E\ a n d\ C F of a triangle A B C intersect at ...

    Text Solution

    |

  12. In the given figure, compute the area of quadilateral

    Text Solution

    |

  13. In Figure, P Q R S is a square and T\ a n d\ U are, respectively, ...

    Text Solution

    |

  14. Compute the area of trapezium P Q R S in Figure

    Text Solution

    |

  15. In Figure, /A O B=90^0,\ A C=B C ,\ O A=12\ c m\ a n d\ O C=6. 5 c mdo...

    Text Solution

    |

  16. In Figure, A B C D is a trapezium in which A B=7c m ,\ A D=B C=5c m ...

    Text Solution

    |

  17. In Figure, O C D E is a rectangle inscribed in a quadrant of a circl...

    Text Solution

    |

  18. In Figure, A B C D is a trapezium in which A B||C D . Prove that: ...

    Text Solution

    |

  19. In Figure, A B C D ,\ A B F E\ a n d\ C D E F are parallelograms. Prov...

    Text Solution

    |

  20. Diagonals A C and B D of a quadrilateral A B C D intersect each a...

    Text Solution

    |