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 ENGLISH|Exercise All Questions|420 Videos
  • TRIGONOMETRIC IDENTITIES

    RD SHARMA ENGLISH|Exercise All Questions|254 Videos

Similar Questions

Explore conceptually related problems

A B C D is a rhombus. Prove that A B^2+B C^2+C D^2+D A^2=A C^2+B D^2

A B C is a triangle in which A B=A C and D is any point in B C . Prove that A B^2-A D^2=B D C D .

In A B C , A D is perpendicular to B C . Prove that: A B^2+C D^2=A C^2+B D^2 (ii) A B^2-B D^2=A C^2-C D^2

If A D is the median of A B C , using vectors, prove that A B^2+A C^2=2(A D^2+C D^2)dot

The perpendicular A D on the base B C of a triangle A B C intersects B C at D so that D B=3C D . Prove that 2\ A B^2=2\ A C^2+B C^2 .

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 fig., if A D_|_B C , prove that A B^2+C D^2=B D^2+A C^2 .

In a right A B C right-angled at C , if D is the mid-point of B C , prove that B C^2=4\ (A D^2-A C^2) .

In /_\ A B C , given that A B=A C and B D_|_A C . Prove that B C^2=2\ A C * C D

In an equilateral A B C , A D_|_B C , prove that A D^2=3\ B D^2

RD SHARMA ENGLISH-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. In an equilateral triangle, prove that three times the square of one s...

    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 if BD=4cm ,D...

    Text Solution

    |

  12. State AA 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 ...

    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=57^0 and /...

    Text Solution

    |

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

    Text Solution

    |