Home
Class 11
MATHS
if diagonals of a parallelogram bisect e...

if diagonals of a parallelogram bisect each other,prove that its a rhombus

Text Solution

Verified by Experts

Let the parallelogram be `= ABCD`
Diagonal `AC` bisect `∠A.`
`∠CAB = ∠CAD`
`AB||CD` and `AC` is a transversal.
...
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE|Exercise Solved Examples And Exercises|361 Videos
  • CONIC SECTIONS

    CENGAGE|Exercise Solved Examples And Exercises|1316 Videos

Similar Questions

Explore conceptually related problems

The diagonals of a parallelogram bisect each other.

The diagonals of a parallelogram bisect each other.

The diagonals of parallelogram bisect each other ( True/ False)

Prove, by vector method, that the diagonals of a parallelogram bisect each other , conversely, if the diagonals of a quadrilateral bisect each other, it is a parallelogram.

Fill in the blanks, in each of the following, so as to make the statement true: A rhombus is a parallelogram in which.... A square is a rhombus in which.... A rhombus has all its sides of ........ length. The diagonals of a rhombus..... each other at... angles. It the diagonals of a parallelogram bisect each other at right angles, then it is a....

Prove by vector method that the diagonals of a parallelogram bisect each other.

If the diagonals of a parallelogram are perpendicular; then it is a rhombus.

Theorem 8.6 : The diagonals of a parallelogram bisect each other.

Theorem 8.7 : If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

Given the following statements : If the diagonals of a quadrilateral bisect each other, then it is a parallelogram. Identify these as contrapositive or converse of each other.

CENGAGE-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-Solved Examples And Exercises
  1. If alpha,beta are the roots of the quadratic equation a x^2+b x=c=0 ...

    Text Solution

    |

  2. If a ,b ,c are non-zero real numbers, then the minimum value of the e...

    Text Solution

    |

  3. if diagonals of a parallelogram bisect each other,prove that its a rho...

    Text Solution

    |

  4. Referred to the principal axes as the axes of co ordinates find the eq...

    Text Solution

    |

  5. If the equation a x^2+b x+c=0(a >0) has two real roots alphaa n db...

    Text Solution

    |

  6. If fig shows the graph of f(x)=a x^2+b x+c ,t h e n Fig a c<0 b. b c ...

    Text Solution

    |

  7. If c!=0 and the equation p//(2x)=a//(x+c)+b//(x-c) has two equal roo...

    Text Solution

    |

  8. If the equation 4x^2-x-1=0a n d3x^2+(lambda+mu)x+lambda-mu=0 have a ro...

    Text Solution

    |

  9. If the equation whose roots are the squares of the roots of the cubic ...

    Text Solution

    |

  10. If the equation a x^2+b x+c=0,a ,b ,c , in R have none-real roots, t...

    Text Solution

    |

  11. If p(q-r)x^2+q(r-p)x+r(p-q)=0 has equal roots, then prove that 2/q=1/p...

    Text Solution

    |

  12. Let alpha,beta in Rdot If alpha,beta^2 are the roots of quadratic e...

    Text Solution

    |

  13. If the ratio of the roots of the equation x^2+p x+q=0 are equal to rat...

    Text Solution

    |

  14. If s intheta,costheta be the roots of a x^2+b x+c=0 , then prove that ...

    Text Solution

    |

  15. If the sum of the roots of the equation 1/(x+a)+1/(x+b)=1//c is zero,...

    Text Solution

    |

  16. Solve the equation x^2+p x+45=0. it is given that the squared differen...

    Text Solution

    |

  17. If alpha,beta are the roots of the equation 2x^2-35x+2=0 , the find ...

    Text Solution

    |

  18. Find a quadratic equation whose product of roots x1a n dx2 is equa...

    Text Solution

    |

  19. If a and b(!=0) are the roots of the equation x^2+a x+b=0, then find...

    Text Solution

    |

  20. If the sum of the roots of the equation (a+1)x^2+(2a+3)x+(3a+4)=0 is -...

    Text Solution

    |