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I and m are t...

Question

I and m are two parallel lines intersected by another pair of parallel lines p and q (see the given figure). Show that $Δ A B C ≅ Δ C D A .$

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Solution

$I n Δ A B C a n d Δ C D A, ∠ B A C = ∠ D C A (A l t e r n a t e i n t e r i o r a n g l e s, a s p | | q) A C = C A (C o m m o n) ∠ B C A = ∠ D A C (A l t e r n a t e i n t e r i o r a n g l e s, a s l | | m) ∴ Δ A B C ≅ Δ C D A (B y A S A c o n g r u e n c e r u l e)$

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