Home
Class 10
MATHS
Prove that the ratio of the areas of two...

Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

If the areas of two similar triangles are equal, prove that they are congruent.

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 median from the vertex of an isosceles triangle is the bisector of the vertical angle.

Prove that if one angle of a triangle is equal to the sum of the other two angles, the triangle is right angled.

If the ratio of the volumes of two spheres is 1:8, then the ratio of their surfaces area is

Prove that the areas of the equilateral triangle described on the side of a square is equal to half the area of the equilateral triangle described on one of its diagonal.

Prove that the sum of any two sides of a triangle is greater than twice the median drawn to the third side.

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

Prove that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

If the volumes of two spheres are in the ratio 6: 27, find the ratio of their surfaces areas.

MBD-TRIANGLES-EXERCISE
  1. Prove that the ratio of the areas of two similar triangles is equal to...

    Text Solution

    |

  2. Fill in the blank ,- The polygons of same number of sides are similar:...

    Text Solution

    |

  3. Fill in the blank ,- The polygons of same number of sides are similar:...

    Text Solution

    |

  4. Fill in the blank ,- All regular polygons of same number of sides are…...

    Text Solution

    |

  5. Fill in the blank ,- A polygon of 10 sides is ………… to a polygon of 11 ...

    Text Solution

    |

  6. In figure, DE is parallel to BC. If (AD)/(DB)=2/3 and AC:= 18 cm find ...

    Text Solution

    |

  7. Given angleABC and DE || BC AD = 4x - 3, DB = 3x - 1 AE = 8x - 7, EC =...

    Text Solution

    |

  8. M and N are points on the sides PQ and PR respectively of anglePQR. If...

    Text Solution

    |

  9. In figure AB = 6 cm, AH = 8 cm, CK = 2.4 cm, BC || HK, calculate AK. ...

    Text Solution

    |

  10. Points P, Q and R lie on sides BC, CA and AB respectively of triangle ...

    Text Solution

    |

  11. Infigure, if AB II DC,find the value of x . .

    Text Solution

    |

  12. In the given figure, DE || BC. If AD = 3.6 cm, AB = 9 cm and AE = 2.4 ...

    Text Solution

    |

  13. In the given figure, DE || BC. If (AD)/(DB)=3/5 AC = 5.6 cm, find AE....

    Text Solution

    |

  14. In the given figure, DE || BC. If AD = x cm, DB = (x - 2) cm, AE = (x...

    Text Solution

    |

  15. In the given figure, AB || PQ and AC || PR. Prove that BC || QR. .

    Text Solution

    |

  16. Examine each pair of triangles in figures and state which pair of tria...

    Text Solution

    |

  17. Examine each pair of triangles in figures and state which pair of tria...

    Text Solution

    |

  18. Examine each pair of triangles in figures and state which pair of tria...

    Text Solution

    |

  19. In fig., angleA=angle1 Prove that triangleBDE~triangleBCA . .

    Text Solution

    |

  20. In figure AB bot BC and DE bot AC. Prove that triangleABC ~ triangleAE...

    Text Solution

    |

  21. A vertical stick 20 cm long casts a shadow 6 cm long on the ground. At...

    Text Solution

    |