l and m are two parallel lines intersected by another pair of parallel lines p and q (see the given figure). Show that ΔABC ≅ ΔCDA.
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Solution
In ΔABC and ΔCDA,
∠BAC = ∠DCA (Alternate interior angles, as p || q)
AC = CA (Common)
∠BCA = ∠DAC (Alternate interior angles, as l || m)
∴ ΔABC ≅ ΔCDA (By ASA congruence rule)
Concept: Criteria for Congruence of Triangles
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