Home
Class 10
MATHS
Prove that three times the sum of the sq...

Prove that three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians of the triangle.

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

Prove that three times the sum of the squares on the sides of a triangle is equal to four times the sum of the square on the medians of the triangle.

Prove that three xx the sum of the squares of the sides of a triangle is equal to fourxx the sum of the squares of the medians of the triangle.

Read the statemenst carefully and state 'T' for true and 'F' for false . 1. If a line divides any two sides of a triangle in the same ratio , then the line is parallel to the third side of the triangle . 2 . The internal bisector of an angle of a triangle divides the opposite side inernally in the ratio of the sides containing the angle . 3 . If a line through one vertex of a triangle divides the opposite in the ratio of other two sides , then the line bisects the angle at the vertex . 4.Any line parallel to the parallel sides dividesproportionally . 5. Two times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians of the triangle .

Three xx the sum of square of the sides of a triangle is equal to four xx the sum of the square of the medians of the triangle.

If the sum of the squares of the sides of triangle is 16 then the sum of the squares of the medians is 3k .Then K is

Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.

Prove that the sum of the squares of the diagonals of parallelogram is equal to the sum of the squares of its sides.

Prove that in a parallelogram, the sum of the squres of the diagonals is equal otthe four times the sum of the square of three conterminos edges.

Prove that the sum of the squares of the diagonals of a rhombus is equal to the sum of the squares of the sides.

Prove that three xx the square of any side of an equilateral-triangle is equal to four xx the square of the altitude.

RD SHARMA-TRIANGLES-All Questions
  1. AD is an altitude of an equilateral triangle ABC. On AD as base...

    Text Solution

    |

  2. A ladder 15 m long reaches a window which is 9m above the ground on on...

    Text Solution

    |

  3. Prove that three times the sum of the squares of the sides of a tri...

    Text Solution

    |

  4. In Figure, D , E are points on sides A B and A C respectively of A...

    Text Solution

    |

  5. In the trapezium ABCD,AC and BD intersect at O and also AB=2CD If the ...

    Text Solution

    |

  6. ABC is an isosceles triangle right-angled at B. Similar triangles ...

    Text Solution

    |

  7. ABC is a right triangle right-angled at B. Let D and E be any points o...

    Text Solution

    |

  8. A girl of height 90 cm is walking away from the base of a lamp-post...

    Text Solution

    |

  9. If A B C is a right triangle right-angled at Ba n dM ,N are the mid-...

    Text Solution

    |

  10. Determine whether the triangle having sides (a-1)c m ,2sqrt(a)c m and ...

    Text Solution

    |

  11. If triangle A B C is similar to triangle D E F such that B C=3C M ...

    Text Solution

    |

  12. The perimeters of two similar triangles are 30cm and 20cm respectively...

    Text Solution

    |

  13. Two triangles B A Ca n dB D C , right angled at Aa n dD respectively, ...

    Text Solution

    |

  14. ABC is a right angle triangle right angled at A. A circle is inscribed...

    Text Solution

    |

  15. In Figure, /B A C=90^0,A D is its bisector. If D E|A c , prove that D...

    Text Solution

    |

  16. Prove that the line segments joints joining the mid-points of the a...

    Text Solution

    |

  17. In figure, P is the mid-point of B C , ,Q is the mid-point of A P ,...

    Text Solution

    |

  18. A vertical stick 12m long casts a shadow 8m long on the ground. At the...

    Text Solution

    |

  19. In a quadrilateral A B C D , if bisectors of the /A B Ca n d/A D C mee...

    Text Solution

    |

  20. In A B C , the bisector of /B meets A C at Ddot A line P Q A C meets...

    Text Solution

    |