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 ENGLISH|Exercise All Questions|306 Videos

  • CONSTRUCTION

    RD SHARMA ENGLISH|Exercise All Questions|40 Videos

Similar Questions

Explore conceptually related problems

In triangle 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 P . Prove that: a r\ ( triangle P B Q)=\ a r\ (triangle \ A R C)

In triangle 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 P . Prove that: a r\ (triangle \ P R Q)=1/2a r\ (triangle \ A R C) .

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 triangle 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 P . Prove that: a r\ ( triangle R Q C)=3/8\ a r\ (triangle \ A B C) .

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 Q . Prove that A Q=Q P .

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 Figure, A P || B Q\ || C R . Prove that a r\ ( A Q C)=\ a r\ (P B R)

In a triangle A B C , let P and Q be points on AB and AC respectively such that P Q || B C . Prove that the median A D bisects P Q .

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 P\ a n d\ B Q are perpendiculars to the line segment A B\ a n d\ A P=B Q . Prove that O is the mid-point of line segment A B\ a n d\ P Q

RD SHARMA ENGLISH-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 Figure, A D=B C\ a n d\ B D=C A. Prove that ∠A D B= ∠B C A a n d ∠D...

    Text Solution

    |

  5. In Figure, A B=A C ,\ D is the point in the interior of A B C such ...

    Text Solution

    |

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

    Text Solution

    |

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

    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 poi...

    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 co...

    Text Solution

    |

  15. In Figure, A D\ |C D\ and C B\ | CD If A Q=B P\ a n d\ D P=C Q , prov...

    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 in the blanks in the following so that each of the following st...

    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

    |