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equal angles lead to equal angles inside a trapezium

Source: Singapore Senior 2008

July 10, 2019
geometrytrapeziumtrapezoidequal angles

Problem Statement

Let ABCDABCD be a trapezium with AD//BCAD // BC. Suppose KK and LL are, respectively, points on the sides ABAB and CDCD such that ∠BAL=∠CDK\angle BAL = \angle CDK. Prove that ∠BLA=∠CKD\angle BLA = \angle CKD.
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