In a quadrilateral ABCD, B=90. If AD2=AB2+BC2+CD2, prove that ACD=90.
B C A D


Answer:


Step by Step Explanation:
  1. Given: A quadrilateral ABCD in which B=90 and AD2=AB2+BC2+CD2.
  2. Here, we have to prove that ACD=90.

    Now, join AC.

    In ΔABC, B=90.  AC2=AB2+BC2 (i) [By Pythagoras' theorem] Now ,AD2=AB2+BC2+CD2AD2=AC2+CD2[ using(i)] Thus, in ΔACD, we have AD2=AC2+CD2.

    Hence, ACD=90[ By converse of pythagoras' theorem ].

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