1. Four Sides: Every quadrilateral has exactly 4 sides

2. Four Angles: Every quadrilateral has exactly 4 angles

3. Four Vertices: Four corner points where sides meet

4. Closed Shape: All sides connect to form a closed figure

Sum of All Angles in a Quadrilateral = 360°

∠A + ∠B + ∠C + ∠D = 360°

Symbol for Parallel: ||

Example: AB || CD means side AB is parallel to side CD

1. Opposite sides are parallel

AB || CD and BC || AD

2. Opposite sides are equal in length

AB = CD and BC = AD

3. Opposite angles are equal

∠A = ∠C and ∠B = ∠D

4. Adjacent angles are supplementary

∠A + ∠B = 180°

5. Diagonals bisect each other

They cut each other in half at the midpoint

Perimeter = 2(a + b)

where a and b are the lengths of two adjacent sides

Area = base × height

Look for: Both pairs of opposite sides are parallel AND equal

Bases: The two parallel sides

Legs: The two non-parallel sides

Height: Perpendicular distance between the bases

Isosceles Trapezoid: Two legs are equal in length, and base angles are equal

Right Trapezoid: Has two adjacent right angles (90°)

Scalene Trapezoid: All four sides have different lengths

Area = ½ × (base₁ + base₂) × height

A = ½ × (b₁ + b₂) × h

Look for: Only ONE pair of parallel sides (not two pairs)

1. All four angles are 90° (right angles)

2. Opposite sides are parallel

3. Opposite sides are equal in length

4. Diagonals are equal in length

5. Diagonals bisect each other

6. Has 2 lines of symmetry

Perimeter = 2(length + width)

P = 2(l + w)

Area = length × width

A = l × w

Look for: Four right angles (90° each) - look for the square corner symbol!

1. All four sides are equal in length

2. Opposite sides are parallel

3. Opposite angles are equal

4. Diagonals bisect each other at right angles (90°)

5. Diagonals bisect the vertex angles

6. Has 2 lines of symmetry (along the diagonals)

Perimeter = 4 × side

P = 4s

Area = ½ × d₁ × d₂

where d₁ and d₂ are the diagonals

Look for: All four sides are equal (like a "tilted square")

1. All four sides are equal in length

2. All four angles are 90°

3. Opposite sides are parallel

4. Diagonals are equal in length

5. Diagonals bisect each other at 90°

6. Has 4 lines of symmetry

Perimeter = 4 × side

P = 4s

Area = side × side

A = s²

• A square is ALWAYS a rectangle (has 4 right angles)

• A square is ALWAYS a rhombus (has 4 equal sides)

• A rectangle is NOT always a square (sides may not be equal)

• A rhombus is NOT always a square (angles may not be 90°)

• All parallelograms are trapezoids (have at least 1 pair of parallel sides)

1. Moving Down = More Specific

A square has MORE properties than a rectangle

2. Moving Up = More General

All shapes below are included in shapes above

3. Special Cases

Square is a special rectangle (with equal sides)

Square is a special rhombus (with right angles)

To Draw a Square:

To Draw a Rectangle:

To Draw a Rhombus:

To Draw a Trapezoid:

✓ All quadrilateral angles always add up to 360°

✓ Parallel lines never meet (use || symbol)

✓ A square is both a rectangle AND a rhombus

✓ All rectangles have 4 right angles (90°)

✓ All rhombuses have 4 equal sides

✓ Trapezoids have exactly ONE pair of parallel sides

✓ Parallelograms have TWO pairs of parallel sides

✓ Opposite sides in a parallelogram are equal

✓ A shape can have multiple names at the same time

✓ Use tick marks (') to show equal sides on diagrams

Parallelogram:

"Para-llel" - has parallel sides!

Rectangle:

"Rect-angle" - has right (90°) angles!

Rhombus:

"Diamond shape" - all sides equal, like a baseball diamond!

Trapezoid:

"Trap has ONE way out" - only ONE pair of parallel sides!

Square:

"Square meal" - everything is EQUAL and RIGHT!

Parallel Sides Count:

• Kite: 0 pairs

• Trapezoid: 1 pair

• Parallelogram: 2 pairs