Home
Class 10
MATHS
In A B C , A D is a median. Prove th...

In ` A B C` , `A D` is a median. Prove that `A B^2+A C^2=2\ A D^2+2\ D C^2` .

Promotional Banner

Topper's Solved these Questions

  • SURFACE AREAS AND VOLUMES

    RD SHARMA|Exercise All Questions|417 Videos

  • TRIGONOMETRIC IDENTITIES

    RD SHARMA|Exercise All Questions|254 Videos

Similar Questions

Explore conceptually related problems

In a quadrilateral A B C D , given that /_A+/_D=90o . Prove that A C^2+B D^2=A D^2+B C^2 .

In figure, ABC is triangle in which /_A B C > 90o and A D_|_C B produced. Prove that A C^2=A B^2+B C^2+2B C.B D .

In figure, ABC is a triangle in which /_A B C=90^@ and A D_|_B C . Prove that A C^2=A B^2+B C^2-2B C.B D .

A point D is taken on the side B C of a \ A B C such that B D=2D Cdot Prove that a r\ (\ A B D)=\ 2\ a r\ (\ A D C)

In figure, AD is a median of a triangle ABC and A M_|_B C . Prove that: (i) A C^2=A D^2+B C.D M+ ((B C)/2)^2 (ii) A B^2=A D^2-B CdotD M+ ((B C)/2)^2 (iii) A C^2+A B^2=2A D^2+ 1/2B C^2

If A B C D is a parallelogram, then prove that a r\ (\ A B D)=\ a r\ (\ B C D)=\ a r\ (\ A B C)=\ a r\ (\ A C D)=1/2\ a r\ (|""|^(gm)A B C D)

The A D ,B Ea n dC F are the medians of a c A B C , then (A D^2+B E^2+C F^2):(B C^2+C A^2+A B^2) is equal to

In a scalene triangle A B C ,D is a point on the side A B such that C D^2=A D D B , sin s in A S in B=sin^2C/2 then prove that CD is internal bisector of /_Cdot

A point D is taken on the side B C of a A B C such that B D=2d Cdot Prove that a r( A B D)=2a r( A D C)dot

In an equilateral triangle A B C if A D_|_B C , then A D^2 = (a)C D^2 (b) 2C D^2 (c) 3C D^2 (d) 4C D^2

RD SHARMA-TRIANGLES-All Questions
  1. In A B C , given that A B=A C and B D|A C . Prove that B C^2=2\...

    Text Solution

    |

  2. A B C D is a rectangle. Points M and N are on B D such that A M|B D...

    Text Solution

    |

  3. In A B C , A D is a median. Prove that A B^2+A C^2=2\ A D^2+2\ D C...

    Text Solution

    |

  4. Prove that in an equilateral triangle, three times the square of a ...

    Text Solution

    |

  5. In a A B C , /A B C=135o . Prove that A C^2=A B^2+B C^2+4\ a r( A ...

    Text Solution

    |

  6. In a quadrilateral A B C D ,\ \ /B=90o . If A D^2=A B^2+B C^2+C D^2...

    Text Solution

    |

  7. In a triangle A B C , N is a point on A C such that B N|A C . If...

    Text Solution

    |

  8. Nazinia is fly fishing in a stream. The tip of her fishing rod is 1...

    Text Solution

    |

  9. State basic proportionality theorem and its converse.

    Text Solution

    |

  10. In the adjoining figure, find A C . (FIGURE)

    Text Solution

    |

  11. In the adjoining figure, if A D is the bisector of /A , what is ...

    Text Solution

    |

  12. State AAA similarity criterion.

    Text Solution

    |

  13. State S S S similarity criterion.

    Text Solution

    |

  14. State S A S similarity criterion.

    Text Solution

    |

  15. In the adjoining figure, D E is parallel to B C and A D=1c m, B D=2c m...

    Text Solution

    |

  16. In the figure given below D E B C . If A D=2. 4 c m , D B=3. 6 c m...

    Text Solution

    |

  17. If the areas of two similar triangles A B C and P Q R are in the ...

    Text Solution

    |

  18. The areas of two similar triangles are 169\ c m^2 and 121\ c m^2 re...

    Text Solution

    |

  19. If A B C and D E F are similar triangles such that /A=57o and /E=73...

    Text Solution

    |

  20. If the altitude of two similar triangles are in the ratio 2:3 , wha...

    Text Solution

    |