Home
Class 9
MATHS
If D, E, f are the mid-point of the side...

If D, E, f are the mid-point of the sides of triangle ABC, prove that : `ar(/_\DEF)=1/4 ar(/_\ABC)`.

Promotional Banner

Topper's Solved these Questions

  • AREA OF PARALLELOGRAMS AND TRIANGLES

    MODERN PUBLICATION|Exercise EXERCISE|83 Videos

  • CIRCLES

    MODERN PUBLICATION|Exercise EXERCISE|94 Videos

Similar Questions

Explore conceptually related problems

D,E and F are the middle points of the sides of the triangle ABC, then

If E, F, G and H are respectively the mid-points of the sides of a parallelogram ABCD, show that ar(EFGH) =1/2 ar(ABCD).

If D,E,F are mid-points of the sides of triangle ABC , prove (by vectors) that area of triangle DEF= 1/4 area of triangle ABC .

E is any point on median AD of a triangle ABC . Show that ar (ABE) = ar (ACE).

ABC and BDE are two equilateral triangles such that D is the mid-point of BC. If AE interesects BC at F, show that : ar(BDE) = 1/4 ar(ABC)

D,E and F are respectively the mid points of the sides AB,BC and CA of a triangle ABC. Prove that by joining these mid points D,E and F and the triangle ABC is divided into four congruent triangles.

D,E and F are mid-points of the sides BC, CA and AB respectively of triangleABC . Prove that ar(triangleDEF) = 1/4 ar (triangleABC)

D,E and F are respectively the mid points of the sides BC,CA and AB of an equilateral triangle ABC, prove that DEF is also equilateral triangle.

MODERN PUBLICATION-AREA OF PARALLELOGRAMS AND TRIANGLES-EXERCISE
  1. If D, E, f are the mid-point of the sides of triangle ABC, prove that ...

    Text Solution

    |

  2. In the figure. Show that ABCD is a parallelogram. Calculate the are...

    Text Solution

    |

  3. Find the area of a rhombus whose diagonals are of lengths 10 cm and 8....

    Text Solution

    |

  4. Calculate the area of trap. PQRS, given in the figure.

    Text Solution

    |

  5. In the figure. ABCD in a trapezium in which AB||DC. Proe that ar(trian...

    Text Solution

    |

  6. In a quad. ABCD it is given that BD = 16 cm. If AL bot BD and CM bot B...

    Text Solution

    |

  7. ABCD is a parallelogram whose diagonals intersect at E. AC is produced...

    Text Solution

    |

  8. ABCD is a parallelogram whose diagonals intersect at E. AC is produced...

    Text Solution

    |

  9. P and Q are respectively the midpoints of sides AB and BC or a triangl...

    Text Solution

    |

  10. P and Q are respectively the midpoints of sides AB and BC or a triangl...

    Text Solution

    |

  11. P and Q are respectively the midpoints of sides AB and BC or a triangl...

    Text Solution

    |

  12. In fig. ABCD and AEFG are two parallelograms. If angleC=55^@ and deter...

    Text Solution

    |

  13. ABCD and AEFD are two parallelograms Prove that: ar(triangleAPE) : a...

    Text Solution

    |

  14. In Fig. ABCD is a parallelogram. Prove that ar (DeltaACP) = ar (Del...

    Text Solution

    |

  15. In triangleABC, it L and M are points on AB and AC respectively such t...

    Text Solution

    |

  16. In triangleABC, it L and M are points on AB and AC respectively such t...

    Text Solution

    |

  17. D and E are points on sides AB and AC respectively of DeltaABC such th...

    Text Solution

    |

  18. D and E are points on sides AB and AC respectively of DeltaABC such th...

    Text Solution

    |

  19. ABCD is parallelogram. X and Y are the mid-points of BC and CD respect...

    Text Solution

    |

  20. PQRS and PABC are two parallelograms of equal area. Prove that QC||BR

    Text Solution

    |

  21. Two parallelograms ABCD and AEFB are drawn on opposite sides of AB. Pr...

    Text Solution

    |