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.
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.
Solution and Explanation
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:
\[ \triangle ABC \cong \triangle CDA \]
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