Question
In the given figure, two parallel line l and m are intersected by two parallel lines p and q.
Show that $\triangle\text{ABC}\cong\triangle\text{CDA}.$
Show that $\triangle\text{ABC}\cong\triangle\text{CDA}.$
✓
Answer
In $\triangle\text{ABC}$ and $\triangle\text{CDA}$
$\angle\text{BAC}=\angle\text{DCA}$ (alternate interior angles for p || q)
$\text{AC = CA}$ (common)
$\angle\text{BCA}=\angle\text{DAC}$ (Alternate interior angles for l || m)
$\therefore\triangle\text{ABC}\cong\triangle\text{CDA}$ (by ASA congruence rule)
$\angle\text{BAC}=\angle\text{DCA}$ (alternate interior angles for p || q)
$\text{AC = CA}$ (common)
$\angle\text{BCA}=\angle\text{DAC}$ (Alternate interior angles for l || m)
$\therefore\triangle\text{ABC}\cong\triangle\text{CDA}$ (by ASA congruence rule)
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