Question

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

Answer 1

In \( \triangle ABC \) and \( \triangle CDA \), we have the following: 

First, we know that:

\[ \angle BAC = \angle DCA \quad \text{(Alternate interior angles, as } p \parallel q) \]

Also, \( AC = CA \) (Common side).

Next, we observe that:

\[ \angle BCA = \angle DAC \quad \text{(Alternate interior angles, as } l \parallel m) \]

Hence, by the **ASA congruence rule**, we conclude that:

\[ \triangle ABC \cong \triangle CDA \]