What is a Parallelogram?

A parallelogram is a quadrilateral with opposite sides parallel and equal. It has special properties related to its sides, angles, and diagonals.

Elements of a Parallelogram

A parallelogram has the following elements:

✅ Sides: Four sides, where opposite sides are equal and parallel.
✅ Angles: Four angles, where opposite angles are equal.
✅ Diagonals: Two diagonals that bisect each other.
✅ Vertices: Four vertices (corners) where two sides meet.

Diagonals of a Parallelogram

A parallelogram has two diagonals, which have the following properties:

✔ Diagonals Bisect Each Other: The diagonals divide each other into two equal halves.
✔ Diagonals Are Not Necessarily Equal: Unlike in a rectangle or square, the diagonals of a parallelogram are usually not equal.

Properties of a Parallelogram

1️⃣ Opposite Sides are Equal

• If ABCD is a parallelogram, then AB = CD and AD = BC.

2️⃣ Opposite Angles are Equal

• ∠A = ∠C and ∠B = ∠D.

3️⃣ Consecutive Angles are Supplementary

• Any two adjacent angles add up to 180°.
• ∠A + ∠B = 180°, ∠B + ∠C = 180°, etc.

4️⃣ Diagonals Bisect Each Other

• If AC and BD are diagonals, then they bisect each other at O, meaning AO = OC and BO = OD.

5️⃣ Each Diagonal Divides the Parallelogram into Two Congruent Triangles

• The two triangles formed by a diagonal are equal in area.

6️⃣ Opposite Sides are Parallel

• By definition, opposite sides of a parallelogram are always parallel.

Key Takeaways

✅ A parallelogram has opposite sides parallel and equal.
✅ Diagonals bisect each other but are generally not equal.
✅ Opposite angles are equal, and adjacent angles are supplementary.
✅ Diagonals divide the parallelogram into two equal triangles.