Home
Class 9
MATHS
In Figure, two sides A B\ a n d\ B C and...

In Figure, two sides `A B\ a n d\ B C` and the median `A D\ ` of ` A B C` are equal respectively to the two sides `P Q\ a n d\ Q R` and the median `P M` of the other triangle `P Q Rdot` Prove that ` A B D~= P Q M` (ii) ` A B C\ ~=\ \ P Q R`

Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    RD SHARMA|Exercise All Questions|306 Videos
  • CONSTRUCTION

    RD SHARMA|Exercise All Questions|29 Videos

Similar Questions

Explore conceptually related problems

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)

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 R Q)=1/2a r\ (\ A R C)

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)

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 Figure, X\ a n d\ Y are the mid-points of A C\ a n d\ A B respectively, Q P\ B C\ a n d\ C Y Q\ a n d\ B X P are straight lines. Prove that a r\ (\ A B P)=\ a r\ (\ A C Q)

In Figure, A B C D\ a n d\ P Q R C are rectangles and Q is the mid-point of A C . Prove that D P=P C (ii) P R=1/2\ A C

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

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 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

RD SHARMA-CONGRUENT TRIANGLE -All Questions
  1. A B C\ a n d\ D B C are two isosceles triangles on the same bas B C...

    Text Solution

    |

  2. A point O is taken inside an equilateral four sided figure A B C D suc...

    Text Solution

    |

  3. In Figure, two sides A B\ a n d\ B C and the median A D\ of A B C ar...

    Text Solution

    |

  4. In the figure AD = BC and BD = CA. Prove that ∠ADB=∠BCA and ∠DAB=∠CBA

    Text Solution

    |

  5. In figure, AB = AC, D is the point in the interior of ABC such that DB...

    Text Solution

    |

  6. In Figure, it is given that A B=C D\ a n d\ A D=B Cdot Prove that A...

    Text Solution

    |

  7. In A P Q R , if P Q=P Q\ a n d\ L ,\ M\ a n d\ N are the mid-points o...

    Text Solution

    |

  8. A D ,\ B E\ a n d\ C F , the altitudes of A B C are equal. Prove that...

    Text Solution

    |

  9. In Figure, it is given that L M=M N ,\ Q M=M R ,\ M L\ |P Q\ a n d\ ...

    Text Solution

    |

  10. If A B C is an isosceles triangle such that A B=A C and A D is an alti...

    Text Solution

    |

  11. P is a point equidistant from two lines l and m intersecting at poin...

    Text Solution

    |

  12. A B C is a triangle and D is the mid-point of B C . The perpendiculars...

    Text Solution

    |

  13. A B C is a triangle is which B E and C F are, respectively, the perpen...

    Text Solution

    |

  14. In perpendiculars from any point within an angle on its arms are con...

    Text Solution

    |

  15. In Figure, A D\ |C D\ and C B\ |c ddot If A Q=B P\ a n d\ D P=C Q , p...

    Text Solution

    |

  16. A B C D is a square, X\ a n d\ Y are points on sides A D\ a n d\ B C r...

    Text Solution

    |

  17. Which of the following statements are true (T) and which are false (...

    Text Solution

    |

  18. Fill the blanks in the following so that each of the following stateme...

    Text Solution

    |

  19. In a A B C ,\ if /A=45^0\ a n d\ /B=70^0dot Determine the shortest ...

    Text Solution

    |

  20. In a A B C , if /A=50^0\ a n d\ /B=60^0 , determine the shortest a...

    Text Solution

    |