Home
Class 9
MATHS
A triangle ABC is given. If lines are ...

A `triangle ABC` is given. If lines are drawn through A, B, C, parallel respectively to the sides BC, CA and AB, forming `triangle PQR`, as shown in the adjoining figure, show that `BC=(1)/(2) QR.`

Text Solution

Verified by Experts

BC||QA and CA||QB `rArr `BCAQ is a ||gm `rArr BC=QA.`
Similarly, BCRA is a ||gm `rArr BC=AR.`
`therefore 2BC = QA+AR=QR.`
Promotional Banner

Topper's Solved these Questions

  • QUADRILATERALS

    RS AGGARWAL|Exercise EXERCISE 10C|18 Videos

  • QUADRILATERALS

    RS AGGARWAL|Exercise Multiple Choice Questions (Mcq)|47 Videos

  • QUADRILATERALS

    RS AGGARWAL|Exercise Exercise 10 A|10 Videos

  • PROBABILITY

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

  • TRIANGLES

    RS AGGARWAL|Exercise MULTIPLE-CHOICE QUESTIONS (MCQ)|10 Videos

Similar Questions

Explore conceptually related problems

Given Delta ABC, lines are drawn through A,B and C parallel respectively to thesides BC,CA and AB, forming Delta PQR( Fig.13.27 ).Show that BC=(1)/(2)QR

Through A, B and C lines RQ, PR and QP have been drawn, respectively parallel to sides BC, CA and AB of a Delta ABC as shown in figure. Show that BC=(1)/(2)QR .

Throuth A,B and C lines RQ, PR and QP have been drawn, respectively parallel to sides BC. CA and AB of a DeltaABC as shown in the given figure. Show that BC=1/2QR.

D, E and F are the mid-points of the sides BC, CA and AB of a triangle ABC. Show that BDEF is a parallelogram

In Delta ABC the lines are drawn parallel to BC,CA and AB respectively through A,B and C intersecting at PQ and R. Find the ration of perimeter of Delta PQR and Delta ABC

Let vec a,vec b,vec c form sides BC,CA and AB respectively of a triangle ABC then

In the adjoining figure D, E and F are the mid-points of the sides BC, AC and AB respectively. triangle DEF is congruent to triangle :

RS AGGARWAL-QUADRILATERALS-EXERCISE 10B
  1. Find the measure of each angle of a parallelogram, if one of its angle...

    Text Solution

    |

  2. ABCD is a parallelogram in which AB=9.5 cm and its perimeter is 30 c. ...

    Text Solution

    |

  3. In each of the figures given below, ABCD is a rhombus. Find the value...

    Text Solution

    |

  4. The length of the diagonals of a rhombus are 24cm and 18cm respectivel...

    Text Solution

    |

  5. Each side of a rhombus is 10 cm long and one of its diagonals measures...

    Text Solution

    |

  6. In each of the figures given below, ABCD is a rectangle. Find the valu...

    Text Solution

    |

  7. A B C D is a rhombus in which the altitude from D to side A B\ bisect...

    Text Solution

    |

  8. In the adjoining figure, ABCD is a square. A line segment CX cuts AB a...

    Text Solution

    |

  9. ABCD is a rhombus. Show that diagonal AC bisects /Aas well as /Cand d...

    Text Solution

    |

  10. In a parallelogram ABCD, points M and N have been taken on opposite si...

    Text Solution

    |

  11. In the adjoining figure, ABCD is a parallelogram.If P and Q are the ...

    Text Solution

    |

  12. In the adjoining figure, ABCD is a parallelogram whose diagonals int...

    Text Solution

    |

  13. The angle between the altitudes of a parallelogram, through the sam...

    Text Solution

    |

  14. ABCD is a rectangle in which diagonal AC bisects /Aas well as /C. Sho...

    Text Solution

    |

  15. In the adjoining figure, ABCD is a parallelogram in which AB is produc...

    Text Solution

    |

  16. In the adjoining figure, ABCD is a parallelogram and E is the midpoint...

    Text Solution

    |

  17. Two parallel lines l and m are intersected by a transversal p (see ...

    Text Solution

    |

  18. K, L, M and N are points on the sides AB, BC, CD and DA respectively...

    Text Solution

    |

  19. A triangle ABC is given. If lines are drawn through A, B, C, parall...

    Text Solution

    |

  20. In the adjoining figure, triangle ABC is a triangle and through A, B, ...

    Text Solution

    |