Question

HELP! WILL GIVE BRAINLIEST! DO NOT TAKE ANSWERS OFF ONLINE, THEY ARE WRONG!!!! The following is an incomplete paragraph proving that the opposite sides of parallelogram ABCD are congruent: Parallelogram ABCD is shown where segment AB is parallel to segment DC and segment BC is parallel to segment AD. 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 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? A) Angles ABC and CDA are corresponding parts of congruent triangles, which are congruent (CPCTC). B) Angles ABC and CDA are congruent according to a property of parallelograms (opposite angles congruent). C) Angles BAC and DCA are congruent by the Same-Side Interior Angles Theorem. D) Angles BAC and DCA are congruent by the Alternate Interior Angles Theorem.

Answer 1

Answer:

The correct option is B.

Step-by-step explanation:

Given information: AB\parallel DCAB∥DC and BC\parallel ADBC∥AD .

Draw a diagonal AC.

In triangle BCA and DAC,

AC\cong ACAC≅AC (Reflexive Property of Equality)

\angle BAC\cong \angle DCA∠BAC≅∠DCA ( Alternate Interior Angles Theorem)

\angle BCA\cong \angle DAC∠BCA≅∠DAC ( Alternate Interior Angles Theorem)

The ASA (Angle-Side-Angle) postulate states that two triangles are congruent if two corresponding angles and the included side of are congruent.

By ASA postulate,

\triangle BCA\cong \triangle DAC△BCA≅△DAC

Therefore option B is correct