The following is an incomplete paragraph proving that the opposite sides of parallelogram ABCD are congruent:
A
B
D
According to the given information, AB || DC and BC || AD. Construct a diagonal from A to C with a straightedge.
Angles BAC and DCA
are congruent by the Alternate Interior Angles Theorem. Angles BCA and DAC are congruent by the Alternate Interior Angles Theorem. Triangles
BCA and DAC are congruent according to the Angle-Side-Angle (ASA) Theorem. By CPCTC, opposite sides AB and CD, as well as sides BC and
DA, are congruent.
Which sentence accurately completes the proof?
Angles BAC and DCA are congruent by the Same-Side Interior Angles Theorem.
Diagonal BD is congruent to itself by the Reflexive Property of Equality
Diagonal AC is congruent to itself by the Reflexive Property of Equality.
Angles ABC and CDA are congruent according to a property of parallelograms ( opposite angels congruent)