Home
Class 9
MATHS
P and Q are any two points lying on the ...

P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD show that `ar(DeltaAPB) = ar Delta(BQC)`

Promotional Banner

Topper's Solved these Questions

  • AREAS OF PARALLELOGRAMS AND TRIANGLES

    KUMAR PRAKASHAN|Exercise Exercise 9.3|10 Videos

  • AREAS OF PARALLELOGRAMS AND TRIANGLES

    KUMAR PRAKASHAN|Exercise Exercise 9.4|5 Videos

  • BOARD'S SAMPLE QUESTION PAPERS (QUESTION PAPER 1 : FOR THE FIRST TEST)

    KUMAR PRAKASHAN|Exercise Section D (Solve the following) |4 Videos

Similar Questions

Explore conceptually related problems

If E, F G and H are respectively the midpoints of the sides AB, BC, CD and AD of a parallelogram ABCD, show that ar(EFGH) =1/2 ar (ABCD) .

In the figure D, E are points on the sides AB and AC respectively of DeltaABC such that ar(DeltaDBC) = ar(DeltaEBC) . Prove that DE || BC.

If P and Q are the middle points of the sides BC and CD of the parallelogram ABCD, then AP+AQ is equal to

E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that DeltaABE ~ DeltaCFB .

P is a point in the interior of a parallelogram ABCD. Show that (i) ar (DeltaAPB) +ar (DeltaPCD)=1/2ar (ABCD) (ii) ar(DeltaAPD)+ar (DeltaPBC)=ar(DeltaAPB)+ar(DeltaPCD) (Hint : Throught , P draw a line parallel to AB)

In the figure, ΔABC, D, E, F are the midpoints of sides BC, CA and AB respectively. Show that (i) BDEF is a parallelogram (ii) ar(DeltaDEF)=1/4ar(DeltaABC) (iii) ar(BDEF)=1/2ar(DeltaABC)

If D ,Ea n dF are three points on the sides B C ,C Aa n dA B , respectively, of a triangle A B C such that AD,BE and CF are concurrent, then show that (B D)/(C D),(C E)/(A E),(A F)/(B F)=-1

ABCD is a trapezium with AB||DC . E and F are points on non-parallel sides AD and BC respectively such that EF is parallel to AB (see the figure). Show that (AE)/(ED)=(BF)/(FC)

In the figure, ΔABC and ΔABD are two triangles on the same base AB. If line segment CD is bisected by bar(AB) at O, show that ar (DeltaABC) = ar (DeltaABD).

KUMAR PRAKASHAN-AREAS OF PARALLELOGRAMS AND TRIANGLES-Multiple Choice Questions (MCQs)
  1. P and Q are any two points lying on the sides DC and AD respectively o...

    Text Solution

    |

  2. Area of a parallelogram =

    Text Solution

    |

  3. Area of a triangle =

    Text Solution

    |

  4. ABCD is a rectangle . If AB=10 cm and ar(ABCD)=150 cm^2 , then BC= cm.

    Text Solution

    |

  5. ABCD is a square . If ar(ABCD)=36 cm^2 . Then AB= cm.

    Text Solution

    |

  6. In triangleABC, BC=10 cm and the length of altitude AD is 5 cm. Then ,...

    Text Solution

    |

  7. In triangleABC, AD is an altitude . If BC=8 cm and ar (ABC)=40 cm^2, t...

    Text Solution

    |

  8. In trianglePQR , PM is an altitude and QR is the hypotenuse. If QR=12 ...

    Text Solution

    |

  9. In triangleXYZ, XZ is the hypotenuse. If XY = 8 cm and YZ=12 cm, then...

    Text Solution

    |

  10. In parallelogram ABCD, AM is an altitude corresponding to base BC. If ...

    Text Solution

    |

  11. In parallelogram PQRS, QR=10 cm and ar(PQRS)=120 cm^2 . Then the lengt...

    Text Solution

    |

  12. For parallelogram ABCD, ar(ABCD)=48 cm^2 . Then ar(ABC)= cm^2

    Text Solution

    |

  13. ABCD is a rhombus . If AC=6cm and BD=9 cm, then ar(ABCD)= cm^2

    Text Solution

    |

  14. PQRS is a rhombus. If ar (PQRS)=40 cm^2 and PR = 8 cm, then QS=cm.

    Text Solution

    |

  15. In trianglePQR, angleQ=90^@, PQ=5 cm and PR=13 cm. Then ar(PQR)= cm^2

    Text Solution

    |

  16. In triangleABC , P,Q and R are the midpoints of AB, BC and CA respecti...

    Text Solution

    |

  17. In triangleABC , P, Q and R are the midpoints of AB, BC and CA respect...

    Text Solution

    |

  18. In triangleABC , P, Q and R are the midpoints of AB, BC and CA respec...

    Text Solution

    |