Question

figure abcd is a parallelogram. which sequence could be used to prove that ad = bc? first prove △abc is congruent to △cda, and then state ad and bc are corresponding sides of the triangles. first prove △abc is similar to △cda, and then state ad and bc are opposite sides of the parallelograms. first prove □abcd is congruent to □cdab, and then state ad and bc are corresponding sides of two parallelograms. first prove □abcd is similar to □cdab, and then state ad and bc are opposite sides of the parallelograms.

Explanation:

• Congruent triangles have corresponding sides equal. If we can prove \(\triangle ABC\cong\triangle CDA\), then the corresponding sides \(AD\) and \(BC\) (where \(AD\) corresponds to \(BC\) in the congruent triangles) will be equal.
• Similar triangles have proportional sides, not necessarily equal. So proving similarity (\(\triangle ABC\sim\triangle CDA\)) won't directly give \(AD = BC\).
• Parallelograms \(ABCD\) and \(CDAB\) are the same parallelogram, so concepts of congruence or similarity of these two (as separate parallelograms) are not relevant in the context of proving \(AD = BC\).

Answer:

First prove \(\triangle ABC\) is congruent to \(\triangle CDA\), and then state \(\overline{AD}\) and \(\overline{BC}\) are corresponding sides of the triangles.