Home
Class 9
MATHS
In figure, ABCD and AEFD are two paralle...

In figure, ABCD and AEFD are two parallelograms. Prove that `ar (DeltaPEA) = ar (DeltaQFD)`.

Text Solution

Verified by Experts

In `triangleRSC and trianglePQB`, we have
`angeCRS = angleBPQ " "("corres". angle)`
`angleCSR = angleBPQ" " ("corres". angle)`
SC = QB (opp. Sides of a ||gm)
`triangleRSC cong trianglePQB` (AAS-criterion).
And so, `ar(triangleRSC)=ar(trianglePQB)`.
Promotional Banner

Topper's Solved these Questions

  • AREAS OF PARALLELOGRAMS AND TRIANGLES

    RS AGGARWAL|Exercise MULTIPLE-CHOICE QUESTIONS (MCQ)|32 Videos

  • AREAS OF PARALLELOGRAMS AND TRIANGLES

    RS AGGARWAL|Exercise ASSERTION & REASON TYPE|5 Videos

  • AREAS OF PARALLELOGRAMS AND TRIANGLES

    RS AGGARWAL|Exercise ASSERTION & REASON TYPE|5 Videos

  • AREAS OF TRIANGLES AND QUADRILATERALS

    RS AGGARWAL|Exercise Multiple Choice Questions (Mcq)|16 Videos

Similar Questions

Explore conceptually related problems

In figure,ABCD and AEFD are two parallelograms.Prove that ar (Delta PEA)=ar(Delta QFD)

In the given figure, ABCD and AEFD a re two parallelograms. ar( Delta PEA) =

In the given figure, ABCD and AEFD a re two parallelograms. PE =

In the figure, ABCD, DCFE and ABFE are parallelograms. Show that ar( Delta ADE) = ar( Delta BCF).

In the figure, ABCD and EFGD are two parallelograms and G is the mid-point of CD. Then, ar (DeltaDPC) = (1)/(2) ar (EFGD) .

In Fig.9.31, ABCD,DCFE and ABFE are parallelograms.Show that ar quad (ADE)=ar(BCF)

In the given figure, ABCD and FECG are parallelograms equal in area. If ar(Delta AQE) = 12 cm^(2) , find ar(||gm FGBQ)

In the figure ABCD and ABFE are Parallelograms then find ar (Delta BCF) . If ar (ABCE) =18 cm^(2) ar (ABCD) =25 cm^(2)

In the given figure, ABCD and ABEF are parallelograms such that ar(quad. EABC) 17 cm^(2) and ar(||gm ABCD) = 25 cm^(2) . Then ar(triangleBCF) = ?

RS AGGARWAL-AREAS OF PARALLELOGRAMS AND TRIANGLES -Exercise 11
  1. O is the any point on diagonal PR of parallelogram PQRS. Prove that Ar...

    Text Solution

    |

  2. In the adjoining figure, the diagonals AC and BD of a quadrilateral AB...

    Text Solution

    |

  3. The vertex A of triangle ABC is joined to a point D on the side BC. Th...

    Text Solution

    |

  4. D is the midpoint of side BC of triangleABC and E is the midpoint of ...

    Text Solution

    |

  5. In trapezium ABCD, AB || DC and L is the mid-point of BC. Through L, a...

    Text Solution

    |

  6. In the adjoining figure, ABCD is a quadrilateral. A line through D, p...

    Text Solution

    |

  7. In the adjoining figure, triangle ABC and triangleDBC are on the same ...

    Text Solution

    |

  8. ABCD is a parallelogram in which BC is produced to E such that CE = BC...

    Text Solution

    |

  9. A point E is taken on the side BC of a parallelogram ABCD. AE and DC a...

    Text Solution

    |

  10. P, Q, R, S are respectively the midpoints of the sides AB, BC, CD and ...

    Text Solution

    |

  11. किसी त्रिभुज ABC की मधिकाएँ CD और BE एक दूसरे को O पर कटती है , तो अन...

    Text Solution

    |

  12. The base BC of Delta ABC is divided at D, so that BD=1/2DC. Prove that...

    Text Solution

    |

  13. In the adjoining figure, BD||CA, E is the midpoint of CA and BD =(1)/(...

    Text Solution

    |

  14. The given figure shows a pentagon ABCDE.EG drawn parallel to DA meets ...

    Text Solution

    |

  15. In figure, CD || AE and CY || BA. Prove that ar (DeltaCBX) = ar (Delta...

    Text Solution

    |

  16. In the adjoining figure, the point D divides the sides of triangleABC ...

    Text Solution

    |

  17. In a trapezium ABCD, AB || DC, AB = a cm, and DC = b cm. If M and N ar...

    Text Solution

    |

  18. ABCD is a trapezium in which AB || DC, AB = 16 cm and DC = 24 cm. If E...

    Text Solution

    |

  19. In figure X and Y are the mid-points of AC and AB respectively, QP || ...

    Text Solution

    |

  20. In figure, ABCD and AEFD are two parallelograms. Prove that ar (DeltaP...

    Text Solution

    |