1. **State the problem:** Given quadrilateral LMNO with sides LM \cong ON and LO \cong MN, prove that LMNO is a parallelogram. 2. **Recall the Parallelogram Side Theorem:** If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. 3. **Given:** - LM \cong ON (opposite sides) - LO \cong MN (opposite sides) 4. **To prove:** LMNO is a parallelogram. 5. **Proof steps:** **Statements:** 1. LM \cong ON and LO \cong MN (Given) 2. Triangles LNO and MNL are congruent (by SSS: LM=ON, LO=MN, LN common side) 3. \angle LNO \cong \angle MNL and \angle NLM \cong \angle OLN (CPCTC - Corresponding Parts of Congruent Triangles are Congruent) 4. Opposite angles are congruent, so LMNO is a parallelogram (Definition of parallelogram) **Reasons:** 1. Given 2. Side-Side-Side (SSS) Congruence Postulate 3. CPCTC 4. Definition of parallelogram 6. **Explanation:** - By showing triangles LNO and MNL are congruent, we establish that opposite angles are congruent. - Congruent opposite sides and angles imply LMNO is a parallelogram. Hence, LMNO is a parallelogram by the Converse of the Parallelogram Side Theorem.