Question

In the given figure, two parallel lines l and m are intersected by two parallel lines p and q.

$\text{Show that}\Delta ABC\cong \Delta CDA.$

Answer 1

ASA(angle side angle):

Two Triangles are congruent if two angles
and the included side of One triangle are equal to two angles & the
included side of the other triangle.


Alternate angles:

When two lines are crossed by another line the
pair of angles on opposite sides of the transversal is called alternate angles.

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Use the properties of a transversal
intersecting two Parallel Lines i.e, interior angles are equal to each other,
to show congruence of given Triangles.



Given,

l || m and p || q


To prove,

$\Delta ABC\cong \Delta CDA$


Proof,

In $\Delta ABCand\Delta CDA$
$\angle BCA=\angle DAC$
(Alternate interior angles as p||q)

AC = CA (Common)


$\angle BAC=\angle DCA$
(Alternate interior angles as l ||m)


Hence, $\Delta ABC\cong \Delta CDA$ (by ASA congruence rule.)