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Diagonal AC of a parallelogram ABCD bis...

Diagonal AC of a parallelogram ABCD bisects `\ /_A`. Show that
(i) it bisects `\ /_C` also,
(ii) ABCD is a rhombus.

Text Solution

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Given: The diagonal AC of a parallelogram ABCD bisects ∠A.
We can use alternate interior angles property to show that the diagonal AC bisects ∠C and by showing all sides are equal, it can be proved ABCD is a rhombus.
i) ABCD is a parallelogram.
`∠DAC = ∠BCA` (Alternate interior angles) ....................(1) ...
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