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:

In parallelogram \(ABCD\), diagonal \(AC\) splits it into \(\triangle ABC\) and \(\triangle CDA\). Since \(ABCD\) is a parallelogram, \(AB \parallel CD\) and \(AD \parallel BC\), leading to \(\angle BAC = \angle DCA\) and \(\angle BCA = \angle DAC\) (alternate interior angles). With common side \(AC\), \(\triangle ABC \cong \triangle CDA\) by ASA. Corresponding sides of congruent triangles are equal, so \(BC = AD\).

Answer:

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