MathematicsState true or false.If a pair of opposite sides of a cyclic quadrilateral are equal, then its diagonals are also equal.

State true or false.


If a pair of opposite sides of a cyclic quadrilateral are equal, then its diagonals are also equal.


  1. A
    True
  2. B
    False 

    Fill Out the Form for Expert Academic Guidance!l



    +91



    Live ClassesBooksTest SeriesSelf Learning



    Verify OTP Code (required)

    I agree to the terms and conditions and privacy policy.

    Solution:

    Given that, a pair of opposite sides of a cyclic quadrilateral are equal.
    Let us assume ABCD   is a cyclic quadrilateral and AD=BC,   then joining AC and BD.
     Considering ΔAOD   and ΔBOC   ,
    AB=BC    {Opposite sides AB   and BC   are equal}
    Since, same segments subtend equal angle to the circle, then the angles are ∠OAD=∠OBCand∠ODA=∠OCB  .
    By ASA congruence rule,
      ΔAOD=ΔBOC..... 1 .  
    Adding ΔDOC   on both sides in equation 1:
    ΔAOD+ΔDOC≅ΔBOC+ΔDOC   ΔADC≅ΔBCD   By CPCT theorem we have, AC=BD  .
    Since we know the diagonals of the given cyclic quadrilateral are equal, therefore, diagonals of the cyclic quadrilateral are equal.
    Hence, the statement is true and option 1 is correct.
     
    Chat on WhatsApp Call Infinity Learn