Neli Tyler has written an incorrect proof to show that quadrilateral ABCD is a parallelogram. He knows segments AB

and DC are congruent. He also knows angles ABC and ADC are congruent. Find the mistake in his proof.

O

Segment AC is congruent to itself, so triangle ABC is congruent to triangle ADC by Side-Angle-Side Triangle

Congruence Theorem. Since the triangles are congruent, so are the corresponding parts, and so angle DAC is

congruent to ACB. In quadrilateral ABCD, AB is congruent to CD and AD is parallel to CB. Since AD is parallel to

CB, alternate interior angles DAC and BCA are congruent. Since alternate interior angles are congruent,

AB must be parallel to CD. Quadrilateral ABCD must be a parallelogram since both pairs of opposite sides are

parallel

B