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 &cong; Δ CDA.

Question

l and m are two parallel lines intersected by another pair of parallel lines p and q(see Fig. 7.19). Show that &Delta; ABC &cong; &Delta; CDA.

Philoid · Accepted Answer

It is given in the figure given,

l parallel to m

And, p parallel to q

To prove:- ΔABC ≅ ΔCDA

∠BCA = ∠DAC (Alternate interior angles)

∠BAC = ∠DCA (Alternate interior angles)

And, side AC is common

Therefore, By ASA congruence,

ΔABC ≅ ΔCDA