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Question
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
l || m ...[Given]
AC is a transversal.
So, ∠DAC = ∠ACB ...[Alternate angles]
p || q ...[Given]
AC is a transversal.
So, ∠BAC = ∠ACD ...[Alternate angles]
Now, △ABC and △CDA,
∠ACB = ∠DAC ...[Proved above]
∠BAC = ∠ACD ...[Proved above]
AC = AC ...[Common]
△ABC ≌ △CDA ...[By AAS congruence rule]
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