Lecture Notes: Properties of Parallelograms

Introduction

• Speaker: Mr. Dallas
• Topic: Properties of Parallelograms
• Definition: A parallelogram is a quadrilateral where opposite sides are parallel.
  • Mnemonic: The word "parallelogram" contains "parallel" to help remember this.

Properties of Parallelograms

There are seven key properties of parallelograms, which apply regardless of the size or location of the parallelogram:

1. Opposite Sides are Parallel

   • This is the defining characteristic of a parallelogram.

2. Opposite Sides are Congruent

   • Congruent means equal in length.
   • Example: Side AB is congruent to side CD, and side AD is congruent to side BC.

3. Opposite Angles are Congruent

   • Opposite angles are equal.
   • Example: If (\angle A = 120^\circ), then (\angle C = 120^\circ).

4. Consecutive Angles are Supplementary

   • Consecutive angles (next to each other) sum to 180 degrees.
   • Example: (\angle A + \angle B = 180^\circ).

5. Diagonals Bisect Each Other

   • Diagonals cut each other into equal parts.
   • Example: Diagonal AC bisects diagonal BD at point E, making AE = EC and BE = ED.

6. One Pair of Sides are Congruent and Parallel

   • Both congruent and parallel sides make it a parallelogram.
   • Cannot mix and match; sides must be both congruent and parallel.

7. Each Diagonal Divides the Quadrilateral into Two Congruent Triangles

   • Diagonals form two equal triangles.
   • Example: Diagonal AC forms two triangles with BC and AB that are congruent.

Conclusion

• Every parallelogram possesses all seven properties.
• Understanding these properties helps in identifying and working with parallelograms.
• Thanks for attending the lecture.