Question

The following is an incomplete paragraph proving that the opposite sides of parallelogram ABCD are congruent:

Answer 1

Observe the given figure,

Parallelogram ABCD is shown where segment AB is parallel to segment DC and segment BC is parallel to segment AD.

We have to prove that the triangles ABC and ADC are congruent.

Since, AC = AC (Reflexive property of Equality)

$\angle BCA = \angle CAD$ (As, ABCD is a parallelogram, so Aternate interior angles are equal)

$\angle ABC = \angle ADC$ (As ABCD is a parallelogram, so opposite angles are always equal)

So, $\Delta ABC \cong \Delta ADC$ by ASA theorem.

So, Option B is the correct answer.