AB = BC = CD = DA
Hence, ABCD is a rhombus.
A parallelogram ABCD's diagonal AC bisects
We could employ the alternative internal angle rule to demonstrate that the diagonal AC bisects C, and by demonstrating that almost all sides are equal, you can conclude ABCD is a rhombus.
i) ABCD is a parallelogram.
∠DAC = ∠BCA (Alternate interior angles)
∠BAC = ∠DCA (Alternate interior angles)
However, it is given that AC bisects ∠A.
∠DAC = ∠BAC
From equations (1), (2), and (3), we obtain
∠DCA = ∠BAC = ∠DAC = ∠BCA
Thus, ∠DCA = ∠BCA
Hence, AC bisects ∠C.
ii) From Equation (4), we obtain
∠DAC = ∠DCA
DA = DC (Side opposite to equal angles are equal)
However, DA = BC and AB = CD (Opposite sides of a parallelogram are equal)
Thus, AB = BC = CD = DA
Hence, ABCD is a rhombus.
Learn more about alternative internal angle rule here: https://brainly.com/question/19486848
#SPJ4
