Question

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

According to the given information, segment AB is parallel to segment DC and segment BC is parallel to segment AD.. Construct a diagonal from A to C with a straightedge. It is congruent to itself by the Reflexive Property of Equality. Angles BAC and DCA are congruent by the Alternate Interior Angles Theorem. Angles BCA and DAC are congruent by the Alternate Interior Theorem. ________________. By CPCTC, opposite sides AB and CD, as well as sides BC and DA, are congruent.

Which sentence accurately completes the proof?

Triangles BCA and DAC are congruent according to the Angle-Angle-Side (AAS) Theorem.
Triangles BCA and DAC are congruent according to the Angle-Side-Angle (ASA) Theorem.
Angles ABC and CDA are congruent according to a property of parallelograms (opposite angles are congruent).
Angles BAD and ADC, as well as angles DCB and CBA, are supplementary by the Same-Side Interior Angles Theorem.

Answer 1

We have to prove that The triangles are congruent, in order to use CPCTC

Answer 2

We know that AC is congruent to itself, and we know 2 angles on both sides of that line, so Angle-side-angle would be what we use to prove the triangles congruent

Answer 3

would it be Triangles BCA and DAC are congruent according to the Angle-Side-Angle (ASA) Theorem then?

Answer 4

Yes