Home
Class 9
MATHS
A B C is a triangle and through A ,\ ...

`A B C` is a triangle and through `A ,\ B ,\ C` lines are drawn parallel to `B C ,\ C A\ a n d\ A B` respectively intersecting at `P ,\ Q\ a n d\ R` . Prove that the perimeter of ` P Q R` is double the perimeter of ` A B C`

Text Solution

Verified by Experts

as we know , line joining mid point of two sides is parallel to third side and
is half of the third side
so here,`PQ||BC`,`QR||AB`and `RP||AC`
`PQ=2xxBC`
`QR=2xxAB`
`PR=2xxAC`
so perimetre of `PQR=PQ+QR+RP`
perimetre of `PQR=2BC+2AB+2AC`
perimetre of `PQR=2(BC+AB+AC)`
...
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    RD SHARMA|Exercise All Questions|67 Videos

  • RATIONALISATION

    RD SHARMA|Exercise All Questions|130 Videos

Similar Questions

Explore conceptually related problems

In a triangle A B C , let P a n d Q be points on A Ba n dA C respectively such that P Q || B C . Prove that the median A D bisects P Qdot

Given A B C , lines are drawn through A ,\ B\ a n d\ C parallel respectively to the sides B C ,\ C A\ a n d\ A B ,\ forming P Q Rdot(F igu r e) .Show that B C=1/2Q R

In a A B C ,\ E\ a n d\ F are the mid-points of A C\ a n d\ A B respectively. The altitude A P\ to\ B C intersects F E\ at Qdot Prove that A Q=Q P

In a triangle, P ,\ Q\ a n d\ R are the mid-points of sides B C ,\ C A\ a n d\ A B respectively. If A C=21\ c m ,\ B C=29 c m\ a n d\ A B=30 c m , find the perimeter of the quadrilateral A R P Q

A B C D is a rhombus and P ,\ Q ,\ R ,\ S are the mid-points of A B ,\ B C ,\ C D ,\ D A respectively. Prove that P Q R S is a rectangle.

In square A B C D ,\ P\ a n d\ Q are mid-point of A B\ a n d\ C D respectively. If A B=8c m\ a n d\ P Q\ a n d\ B D intersect at O , then find area of O P B

A B C D is a parallelogram, E\ a n d\ F are the mid-points of A B\ a n d\ C D respectively. G H is any line intersecting A D ,\ E F\ a n d\ B C at G ,\ P\ a n d\ H respectively. Prove that G P=P H

In A A B C ,\ P\ a n d\ Q are respectively the mid-points of A B\ a n d\ B C and R is the mid-point of A Pdot Prove that: a r\ ( R Q C)=3/8\ a r\ (\ A B C)

In Figure, B E_|_A C ,\ A D is any line from A\ to\ B C intersecting B E in HdotP ,\ Q\ a n d\ R are respectively the mid-points of A H ,\ A B\ a n d\ B Cdot Prove that /_P Q R=90^0

In A A B C ,\ P\ a n d\ Q are respectively the mid-points of A B\ a n d\ B C and R is the mid-point of A Pdot Prove that: a r\ ( P B Q)=\ a r\ (\ A R C)

RD SHARMA-QUADRILATERALS-All Questions
  1. In Figure, triangle A B C is right-angled at Bdot Give that A B=9C M ,...

    Text Solution

    |

  2. In Figure, M ,\ N\ a n d\ P are the mid-points of A B ,\ A C\ a n d\ B...

    Text Solution

    |

  3. A B C is a triangle and through A ,\ B ,\ C lines are drawn para...

    Text Solution

    |

  4. In Figure, B E|A C ,\ A D is any line from A\ to\ B C intersecting B E...

    Text Solution

    |

  5. In figure A B=A C\ a n d\ C P||B A and A P is the bisector of exter...

    Text Solution

    |

  6. Let A B C be an isosceles triangle in which AB=AC If D , E , F be th...

    Text Solution

    |

  7. A B C is a triangle. D is a point on A B such that D=1/4A B\ a n d\ E ...

    Text Solution

    |

  8. In Figure, A B C D is a parallelogram in which P is the mid-point o...

    Text Solution

    |

  9. In Figure, A B C D\ a n d\ P Q R C are rectangles and Q is the mid-poi...

    Text Solution

    |

  10. A B C D is a parallelogram, E\ a n d\ F are the mid-points of A B\ a n...

    Text Solution

    |

  11. B M\ a n d\ C N are perpendicular to a line passing through the vert...

    Text Solution

    |

  12. Show that the line segments joining the mid-points of the opposite s...

    Text Solution

    |

  13. Fill in the blanks to make the following statements correct The tr...

    Text Solution

    |

  14. In a parallelogram A B C D , write the sum of angle A\ a n d\ B

    Text Solution

    |

  15. In a parallelogram A B C D , if /D=115^@, then write the measure of ...

    Text Solution

    |

  16. P Q R S is a square such that P R\ a n d\ S Q intersect at Odot State ...

    Text Solution

    |

  17. In a quadrilateral A B C D , bisectors of angles A\ a n d\ B intersect...

    Text Solution

    |

  18. The diagonals of a rectangle A B C D\ meet at O . If /B O C=44^@, f...

    Text Solution

    |

  19. If P Q R S is a square, then write the measure of /S R P

    Text Solution

    |

  20. If A B C D is a rectangle with /B A C=32^@, find the measure of /D B C

    Text Solution

    |