An isosceles triangle BCD is given. From the vertex of angle C, the bisector CA is drawn

An isosceles triangle BCD is given. From the vertex of angle C, the bisector CA is drawn. Angle CBA = Angle BCA. Prove that BA = AC.

Before proving that BA is equal to AC, pay attention to the fact that in ΔABC the angle CBA is equal to the angle BCA.
Hence it follows that ΔABC is isosceles.
According to the rule, in an isosceles triangle, the angles at the base are equal.
Thus, in isosceles ΔABC, the sides BA and AC are equal, as required.



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