Home
Class 9
MATHS
A B C D is a parallelogram, if the two d...

`A B C D` is a parallelogram, if the two diagonals are equal, find the measure of `/_A B Cdot`

Text Solution

Verified by Experts

Since ABCD is a parallelogram. Therefore,`AB=CD` and `AD=BC`
Thus, in `△ABD `and` △ ACB`,`AD=BC`
`BD=AC`
`AB=AB`
So, by SSS criterion of congruence,`△ABD≅△ACB`
Therefore, `∠BAD=∠ABC`
Now, `AD∥BC` and transversal AB intersects them at A and B respectively
Therefore,`∠BAD+∠ABC=180@`
`∠ABC+∠ABC=180@`
`2∠ABC=180@`
`∠ABC=90@`
Hence, the measure of `∠ABC is 90@`.
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    RD SHARMA|Exercise All Questions|306 Videos

  • CONSTRUCTION

    RD SHARMA|Exercise All Questions|29 Videos

Similar Questions

Explore conceptually related problems

In a parallelogram, if the diagonals are equal, then the parallelogram necessarily will be

In parallelogram ABCD, diagonals AC and BD are equal. Find the measure of angle ABC and prove that the quadrilateral ABCD is a rectangle.

In a parallelogram A B C D , if /_D=115^0, then write the measure of /_A

ABCD is a parallelogram with AC and BD as diagonals. Then, A vec C - B vec D =

A B C D is a parallelogram. E is a point on B A such that B E=2\ E A\ a n d\ F is a point on D C such that D F=2\ F Cdot Prove that A E\ C F is a parallelogram whose area is one third of the area of parallelogram A B\ C Ddot

A B C D is a parallelogram whose diagonals intersect at Odot If P is any point on B O , prove that: a r\ ( A D O)=A R\ ( C D O) a r\ (\ A B P)=\ a r\ (\ C B P)

A diagonal of a parallelogram divides it into two triangles of equal area.

A B C D is a parallelogram in which diagonal A C\ bisects /_B A Ddot If /_B A C=35^0 , then /_A B C= 70^0 (b) 110^0 (c) 90^0 (d) 120^0

A B C D is a parallelogram, M is the mid-point of B D and B M bisects /_B . Then, /_A M B= 45^0 (b) 60^0 (c) 90^0 (d) 75^0

RD SHARMA-CONGRUENT TRIANGLE -All Questions
  1. A B C and D B C are two isosceles triangles on the same base B C ...

    Text Solution

    |

  2. Explain -Side Side Side(SSS) Congruence .

    Text Solution

    |

  3. A B C D is a parallelogram, if the two diagonals are equal, find th...

    Text Solution

    |

  4. In a A B C , it is given that A B=A C and the bisectors of /B a...

    Text Solution

    |

  5. A B C is a triangle in which /B =2 /CdotD is a point on B C s...

    Text Solution

    |

  6. In A B C ,\ /A=100^0a n d\ A B=A Cdot Find /B\ a n d\ /C

    Text Solution

    |

  7. In Figure, A B=A C\ a n d\ /A C D=120^0dot Find /A

    Text Solution

    |

  8. Prove that measure of each angle of an equilateral triangle is 60^0d...

    Text Solution

    |

  9. In Figure O is the mid-point of A B\ a n d\ C Ddot Prove that \ A O C...

    Text Solution

    |

  10. In Figure, it is given that A B=C F ,\ E F=B D\ a n d\ /A F E=\ /C B...

    Text Solution

    |

  11. In Figure, it is given that A E=A D\ a n d\ B D=C Edot Prove that A...

    Text Solution

    |

  12. Given: In /\ABC and /\PQR, A B=P Q ,\ B C=Q R\ a n d\ C B\ a n d\ R ...

    Text Solution

    |

  13. In Figure, X ,\ Y\ are two points on equal sides A B\ a n d\ A C of...

    Text Solution

    |

  14. Suppose line segments A B\ a n d\ C D intersect at O in such a way tha...

    Text Solution

    |

  15. If D is the mid-point of the hypotenuse A C of a right triangle A B ...

    Text Solution

    |

  16. A B is a line segment and line l is its perpendicular bisector. If a...

    Text Solution

    |

  17. In quadrilateral A C B D ,\ A C=A D\ a n d\ A B\ bisects /A . Show th...

    Text Solution

    |

  18. Prove that A B C is isosceles if any one of the following holds: (i...

    Text Solution

    |

  19. In Figure, P Q R S is a quadrilateral and T\ a n d\ U are respectively...

    Text Solution

    |

  20. In Figure, P S=Q R\ a n d\ /S P Q=/R Q Pdot Prove that P Q S\ ~=\ Q...

    Text Solution

    |