# l and m are two parallel lines intersected by another pair of parallel lines p and q(see Fig. 7.19). Show that Δ ABC ≅Δ CDA.

It is given in the figure given,

l parallel to m

And, p parallel to q

To prove:- ΔABC ≅ ΔCDA
In ΔABC and ΔCDA

BCA = DAC (Alternate interior angles)

∠BAC = ∠DCA (Alternate interior angles)

AC = AC (common)

Two angles and one side in between are equal, therefore, By ASA congruence,

ΔABC ≅ ΔCDA

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