Step-by-step explanation:
Statement . . . . Reason
1. AB ║ LD . . . . definition of parallelogram*
2. ∠LKC ≅ ∠AKB . . . . vertical angles are congruent
3. ∠BAK ≅ ∠CLK . . . . alternate interior angles at a transversal are congruent
4. ΔABK ~ ΔLCK . . . . AA similarity postulate
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* We suppose that ABCD being a parallelogram shows only that CD║AB. However, point L is shown as being on line CD, so we can claim AB║LD by virtue of the fact that opposite sides of a parallelogram are parallel, and any part of one parallel line is parallel to any part of the other one.