ABCD is a parallelogram with AB = 10 and AD = 6. The bisector of angle A meets side DC at the point E. What is the length of EC?

Since AB ∥ DC, angle AED = angle EAB (alternate angles). The bisector gives angle EAB = angle DAE, so angle AED = angle DAE and triangle ADE is isosceles with DE = AD = 6. As DC = AB = 10, EC = 10 − 6 = 4.