Question

In the given figure, two parallel lines l and m are intersected by two parallel lines p and q. Show that △ ABC ≅ △ CDA.

Answer 1

Based on the △ ABC and △ CDA

We know that p || q and ∠ BAC and ∠ DCA are alternate interior angles

So we get

∠ BAC = ∠ DCA

We know that A and C are the common points for all the lines

So it can be written as

AC = CA

We know that l || m and ∠ BCA and ∠ DAC are alternate interior angles

So we get

∠ BCA = ∠ DAC

Therefore, by ASA congruence rule it is proved that

△ ABC ≅ △ CDA