Quadrilaterals - Master Geometry

Properties of Parallelograms and Special Quadrilaterals

Welcome to Quadrilaterals Mastery!

Let's Explore!

Discover the fascinating properties of parallelograms, rectangles, rhombuses, and more! Choose a lesson below to begin your geometric journey!

Key Concepts & Theorems

Parallelogram Definition

📐

A parallelogram is a quadrilateral with both pairs of opposite sides parallel.

Properties:
  • Opposite sides are parallel
  • Opposite sides are equal
  • Opposite angles are equal
  • Diagonals bisect each other

Diagonal Theorem

In a parallelogram, the diagonals bisect each other.

Proof:

Using ASA congruence rule, we can prove that triangles formed by diagonals are congruent, making the diagonals bisect each other.

Opposite Sides Property

↔️

In a parallelogram, opposite sides are both parallel and equal in length.

Mathematically:

AB ∥ DC and AB = DC
AD ∥ BC and AD = BC

Opposite Angles Property

🔄

In a parallelogram, opposite angles are equal.

Mathematically:

∠A = ∠C and ∠B = ∠D

Special Quadrilaterals

Special types of parallelograms with additional properties.

Types:
  • Rectangle: All angles are 90°
  • Rhombus: All sides are equal
  • Square: All sides equal + all angles 90°

Area Formula

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The area of a parallelogram can be calculated using base and height.

Formula:

Area = base × height

A = b × h