Question

Question 6 (i)
Diagonal AC of parallelogram ABCD bisects $\angle$ A ( see the given figure). Show that
It bisects $\angle$ C also,

Answer 1

ABCD is a parallelogram
$\angle DAC=\angle BCA$ (Alernate interior angles) ….(1)
And, $\angle BAC=\angle DCA$ (Alternate interior angles) …..(2)
However, it is given that AC bisects $\angle$A.
$\angle DAC=\angle BAC$ …(3)
From equations (1) ,(2) and (3), we obtain
$\angle DAC=\angle BCA=\angle BAC=\angle DCA$ …(4)
$\angle DCA=\angle BCA$
Hence, AC bisects $\angle C$.