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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