Question
$l$ and $m$ are two parallel lines intersected by another pair of parallel lines $p$ and $q$. Show that $\Delta ABC \cong \Delta CDA.$
✓
Answer
Given : $l || m$ and $p || q$
To prove : $DABC \cong DCDA$
Proof : $l || m$ and $p || q . . . . [$Given$]$
In $DABC$ and $DCDA$
$ \angle BAC = \angle DCA . . . . . [$Alternate interior angles as $AB || DC]$
Similarly, $\angle ACB = \angle CAD . . . [$Alternate interior angles as $BC || DA]$
$AC = DA . . . [$Common$]$
$DABC \cong DCDA [$By $ASA$ congruency$]$
To prove : $DABC \cong DCDA$
Proof : $l || m$ and $p || q . . . . [$Given$]$
In $DABC$ and $DCDA$
$ \angle BAC = \angle DCA . . . . . [$Alternate interior angles as $AB || DC]$
Similarly, $\angle ACB = \angle CAD . . . [$Alternate interior angles as $BC || DA]$
$AC = DA . . . [$Common$]$
$DABC \cong DCDA [$By $ASA$ congruency$]$
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