Properties of Parallelograms

Definition of a Parallelogram

• A quadrilateral where opposite sides are parallel.
• It is a four-sided polygon with two pairs of parallel sides.
• Mnemonic: The word "parallelogram" contains "parallel," indicating its defining feature.

Seven Properties of Parallelograms

Parallelograms possess seven key properties or characteristics:

1. Opposite Sides are Parallel

• This is the defining characteristic of a parallelogram.

2. Opposite Sides are Congruent

• "Congruent" means equal in length.
• Example: If side AB = 5 inches, then side CD = 5 inches; if AD = 3 inches, then BC = 3 inches.

3. Opposite Angles are Congruent

• Angles opposite each other are equal.
• Example: If angle A = 120°, then angle C = 120°; if angle B = 60°, then angle D = 60°.

4. Consecutive Angles are Supplementary

• "Consecutive" means next to each other.
• "Supplementary" means they add up to 180°.
• Example: If angle A = 120°, angle B = 60°, then A + B = 180°.

5. Diagonals Bisect Each Other

• A diagonal is a line segment joining two non-adjacent vertices.
• "Bisect" means to divide into two equal parts.
• Example: Diagonal AC bisects diagonal DB. If AC = 20 cm, then AE = 10 cm and EC = 10 cm.

6. One Pair of Sides are Congruent and Parallel

• One set of opposite sides are both equal in length and parallel.
• Cannot mix and match sides; both conditions must be satisfied simultaneously.

7. Each Diagonal Divides the Parallelogram into Two Congruent Triangles

• Each diagonal creates two triangles that are congruent (equal in size and shape).

Conclusion

• All parallelograms possess these seven properties.
• Regardless of size or location, these characteristics are consistent.

Final Note

Remember, understanding these properties will help in identifying and working with parallelograms in various mathematical contexts. Every parallelogram has all the aforementioned properties.