In-Depth Notes on Quadrilaterals

Quadrilaterals Notes

Quadrilaterals Overview

• A quadrilateral is a 4-sided shape.

  • Interior angle sum: 360°

  • Exterior angle sum: 360°

  • Equation: ( A + B + C + D = 360° )

  • This holds true for ALL quadrilaterals.

Types of Quadrilaterals

• Parallelograms: 2 pairs of parallel sides.

  • Types of parallelograms:

  1. Rectangle

  2. Rhombus

  3. Square

• Non-parallelograms:

  • Kites

  • Trapezoids

Kites

• A kite is characterized by:

  1. Two pairs of congruent sides.

  2. One pair of congruent angles.

  3. Diagonals intersect at right angles.

  4. The shorter diagonal is bisected by the longer diagonal.

Trapezoids

• A trapezoid has:

  1. One pair of parallel sides (bases).

  2. One pair of non-parallel sides (legs).

  3. Consecutive angles between bases are supplementary:

  • ( A + D = 180° )

  • ( B + C = 180° )

• Types of Trapezoids:

  • Isosceles (legs are congruent)

  • Right trapezoid (two right angles)

  • Non-Isosceles

Parallelograms

• Properties:

  1. 2 pairs of parallel sides.

  2. Opposite sides are congruent.

  3. Opposite angles are congruent.

  4. Consecutive angles are supplementary.

  5. Diagonals bisect each other.

• Symmetry: Rotating 180° brings it back to the same position.

Rectangles

• Inherit all properties of parallelograms plus:

  1. Four right angles.

  2. Diagonals are congruent.

Rhombuses

• Inherit all properties of parallelograms plus:

  1. Four congruent sides.

  2. Diagonals are perpendicular.

  3. Diagonals bisect angles.

Squares

• Inherit properties from both rectangles and rhombuses:

  • 4 right angles,

  • Congruent diagonals,

  • All properties of rectangles and rhombuses.

Venn Diagram Summary

• Rhombuses: Four congruent sides, diagonals perpendicular.

• Rectangles: Four right angles, diagonals congruent.

• Squares: Both properties of rhombuses and rectangles.