ABCD is a parallelogram, if the two diagonals
are
equal. Find the measure of LABC ,
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Answer:
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
o
∠ABC+∠ABC=180
o
2∠ABC=180
o
∠ABC=90
o
Hence, the measure of ∠ABC is 90
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