In the figure, it is given that AE = AD and BD = CE. Prove that △AEB is congruent △ADC.
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Solution
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We have AE=AD and CE=BD. Adding, we get AE+CE=AD+BD ⇒AC=AB. In triangles AEB and ADC, we have AE=AD ....... (given); AB=AC ....... (proved); ∠EAB=∠DAC, (common angle). By SAS postulate △AEB≅△ADC.
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