**Answer:**

SAS rule

**Step-by-step explanation:**

**To prove: **A quadrilateral ABCD is a parallelogram.

**Proof:** It is given that ABCD is an equilateral, thus side AB is parallel to side DC so the alternate interior angles are congruent, thus ∠ABD and ∠BDC, are congruent.

Also, From ΔADB and ΔCDB, we have

AB=DC (Given)

∠ABD =∠BDC (Alternate angles)

DB=DB (Common)

Thus, **by SAS rule of congruency, ΔADB is congruent to ΔCDB that is ΔADB≅ΔCDB.**

By CPCTC, ∠DBC and ∠ADB are congruent and sides AD and BC are congruent. ∠DBC and ∠ADB form a pair of alternate interior angles.

Therefore, AD is congruent and parallel to BC.

**Quadrilateral ABCD is a parallelogram because its opposite sides are equal and parallel.**

**Hence proved.**