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Question

In the given figure, if AB = CD and BC = DA, then which of the following is true?


  1.  ABCCDA by SSS postulate

  2. ABCCDA by SSS postulate

  3.  AB // CD

  4.  BC // AD


Solution

The correct options are
B

ABCCDA by SSS postulate


C

 AB // CD


D

 BC // AD


In ABC and ADC

(i) AB = CD ..... (given)

(ii) BC = DA ..... (given)

(iii) AC = AC ..... (common)

(iv) ABCADC ..... (SSS Postulate)

(v) BAC=DCA  .....(cpct)

 ABCD ......(alternate angles are equal)

(vi) BCA = DAC .....(cpct)

  BCAD .....(alternate angles are equal)

Hence (B), (C) and (D)

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