MathematicsState true or false:In the given figure, if EAEC=EBED, then ΔEAB ∼ ΔECD.

State true or false:


In the given figure, if EAEC=EBED, then ΔEAB ∼ ΔECD.


  1. A
    True
  2. B
    False 

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    Solution:

    It is given that EAEC=EBED.
    Converse of basic proportionality theorem states that if any line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.
    It is given that EAEC=EBED.
    So, EAEB=ECED.
    In ΔEAB and ΔECD,
    EAEB=ECED
    ∠AEB=∠DEC    (Vertically opposite angles)
    ⇒ΔEAB ∼ ΔECD       (By SAS similarity criterion)
    Therefore, it is true that in the given figure, if EAEC=EBED, then ΔEAB ∼ ΔECD.
    Hence, option 1 is correct.   
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