Home
Class 10
MATHS
In a quadrilateral A B C D , given ...

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` .

Text Solution

AI Generated Solution

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

In a cyclic quadrilateral A B C D , if /_A=3 /_C . Find /_A

In an equilateral A B C , A D_|_B C , prove that A D^2=3\ B D^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 a quadrilateral A B C D , /_B=90^o , A D^2=A B^2+B C^2+C D^2 , prove that /_A C D=90^o

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 .

The diagonals of quadrilateral A B C D intersect at O . Prove that (a r( A C B))/(a r( A C D))=(B O)/(D O)

In a quadrilateral A B C D ,\ \ /_B=90o . If A D^2=A B^2+B C^2+C D^2 then prove that /_A C D=90o .

In a quadrilateral A B C D ,C O and D O are the bisectors of /_C and /_D respectively. Prove that /_C O D=1/2(/_A+/_B)dot

If A B C D is a quadrilateral in which A B C D and A D=B C , prove that /_A = /_B .

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

RD SHARMA ENGLISH-TRIANGLES-All Questions
  1. A point D is on the side B C of an equilateral triangle A B C su...

    Text Solution

    |

  2. In A B C , if B D|A C and B C^2=2\ A C C D , then prove that A B=...

    Text Solution

    |

  3. In a quadrilateral A B C D , given that /A+/D=90o . Prove tha...

    Text Solution

    |

  4. In /\ A B C , given that A B=A C and B D|A C . Prove that B C^2=2\...

    Text Solution

    |

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

    Text Solution

    |

  6. 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

    |

  7. In an equilateral triangle, prove that three times the square of one s...

    Text Solution

    |

  8. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  12. State basic proportionality theorem and its converse.

    Text Solution

    |

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

    Text Solution

    |

  14. In the adjoining figure, if A D is the bisector of /A if BD=4cm ,D...

    Text Solution

    |

  15. State AA similarity criterion.

    Text Solution

    |

  16. State S S S similarity criterion.

    Text Solution

    |

  17. State S A S similarity criterion.

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |