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l and m are two parallel lines intersected by another pair of parallel lines p and q. Show that ΔABC ≅ ΔCDA.

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l and m are two parallel lines intersected by another pair of parallel lines p and q. Show that ΔABC ≅ ΔCDA.

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Given that l // m; p // q. 

In ΔABC and ΔCDA 

∠BAC = ∠DCA (∵ alternate interior angles) 

∠ACB = ∠CAD AC = AC 

∴ ΔABC ≅ ΔCDA (∵ ASA congruence)

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