An isosceles triangle has two equal sides and two equal base angles.
Given that : AK = KC and MN∥ AC
ΔMNB is similar to ΔACB (congruence property)
ΔANB = ΔANC (SAS congruence property)
ΔCMB = ΔCMA (SAS congruence property)
= (Angle bisector theorem)
<BAC = <ACB (base angle property of an isosceles triangle)
/AB/ = /BC/ (side property of an isosceles triangle)
Therefore, ΔABC is an isosceles triangle.
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