*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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