In the given figure, two parallel line l and m are intersected by two parallel lines p and q.
Question:

In the given figure, two parallel line l and m are intersected by two parallel lines p and q.
Show that ΔABC ≅ ΔCDA.

 

Solution:

Given: In the given figure, two parallel line l and m are intersected by two parallel lines p and q.

To prove: ΔABC ≅ ΔCDA

Proof:
In ΔABC and ΔCDA,

BAC = DCA           (Alternate interior angles, pq)
BCA = DAC           (Alternate interior angles, lm)
AC = CA                        (Common side)

 By ASA congruence criteria,
ΔABC ≅ ΔCDA

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