This document defines and provides properties of parallelograms, rhombi, rectangles, and squares. Parallelograms have both pairs of opposite sides that are congruent and consecutive angles that are supplementary. Rhombi are parallelograms with four congruent sides. Rectangles are parallelograms with four right angles. Squares are parallelograms with four congruent sides and four right angles.

2. Both pairs of opposite sides are congruent
Consecutive angles are supplementary
Opposite angles are congruent

3.  Given:
 Prove: ABCD is a parallelogram

4.  Given:
 Prove: EFGH is a parallelogram

5.  Given:
 Prove: DEFG is a parallelogram

6.  Rhombus – parallelogram with four congruent
sides
Notations for angles:
∠𝐴 ≅ ∠𝐶
∠𝐷 ≅ ∠𝐵
Notations for sides:
𝐴𝐵 ≅ 𝐵𝐶 ≅ 𝐶𝐷 ≅ 𝐷𝐴
𝐴𝐵 ∥ 𝐷𝐶 and 𝐴𝐷 ∥ 𝐵𝐶

7.  rectangle– parallelogram with four right
angles
Notations for angles:
∠𝐸, ∠𝐹, ∠𝐺 𝑎𝑛𝑑 ∠𝐻 𝑎𝑟𝑒 90°
Notations for sides:
𝐸𝐹 ≅ 𝐻𝐺
𝐸𝐻 ≅ 𝐹𝐺
𝐸𝐻 ∥ 𝐹𝐺 and 𝐸𝐻 ∥ 𝐹𝐺

8.  Square – parallelogram with four congruent
sides and four right angles
Notations for angles:
∠𝐴, ∠𝐵, ∠𝐶 𝑎𝑛𝑑 ∠𝐷 𝑎𝑟𝑒 90°
Notations for sides:
𝐴𝐵 ≅ 𝐵𝐶 ≅ 𝐶𝐷 ≅ 𝐷𝐴
𝐴𝐵 ∥ 𝐷𝐶 and 𝐴𝐷 ∥ 𝐵𝐶