Home
Class 10
MATHS
In A B C , A D is perpendicular to B...

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`

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

A B C is a triangle. D is the mid point of B Cdot If A D is perpendicular to A C , then prove that cos A\ dotcos C=(2(c^2-a^2))/(3a c) .

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 .

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

A B D is a right triangle right-angled at A and A C_|_B D . Show that A B^2=B CdotB D (ii) A C^2=B CdotD C (iii) A D^2=B DdotC D (iv) (A B^2)/(A C^2)=(B D)/(D C)

In Figure, ABD is a triangle right-angled at A and A C_|_B D . Show that (i) A B^2=B C.B D (ii) A C^2=B C.D C (iii) A D^2=B D.C D

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 .

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)

RD SHARMA-TRIANGLES-All Questions
  1. In an isosceles triangle A B C with A B=A C , B D is perpendicul...

    Text Solution

    |

  2. A B C is a triangle in which A B=A C and D is any point in B C ....

    Text Solution

    |

  3. In A B C , A D is perpendicular to B C . Prove that: A B^2+C D^...

    Text Solution

    |

  4. From a point O in the interior of a A B C , perpendiculars O...

    Text Solution

    |

  5. A point O in the interior of a rectangle A B C D is joined with ...

    Text Solution

    |

  6. 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^...

    Text Solution

    |

  7. In a triangle A B C ,\ A C > A B , D is the mid-point of B C and A...

    Text Solution

    |

  8. In a triangle A B C ,\ A C > A B , D is the mid-point of B C and...

    Text Solution

    |

  9. In an equilateral triangle A B C the side B C is trisected at D ...

    Text Solution

    |

  10. In a A B C ,\ \ A D|B C and A D^2=B DxxC Ddot Prove that A B C is a ...

    Text Solution

    |

  11. P and Q are points on the sides C A and C B respectively of A B C, ri...

    Text Solution

    |

  12. A B C is an isosceles triangle with A C=B C . If A B^2=2\ A C^2 , p...

    Text Solution

    |

  13. In P Q R ,\ \ Q M|P R and P R^2-P Q^2=Q R^2 . Prove that Q M^2=P M...

    Text Solution

    |

  14. Prove that the sum of the squares of the diagonals of parallelogram...

    Text Solution

    |

  15. If the sides of a triangle are 3 cm, 4 cm and 6 cm long, determine ...

    Text Solution

    |

  16. The sides of certain triangles are given below. Determine which of ...

    Text Solution

    |

  17. A man goes 15 metres due west and then 8 metres due north. How far ...

    Text Solution

    |

  18. A ladder 17m long reaches a window of a building 15m above the grou...

    Text Solution

    |

  19. Two poles of heights 6 m and 11 m stand on a plane ground. If the d...

    Text Solution

    |

  20. In an isosceles triangle A B C ,\ A B=A C=25 c m ,\ \ B C=14 c m . ...

    Text Solution

    |