Quadrilaterals Beginner

Master the four-sided polygons: parallelograms, rectangles, rhombi, squares, and trapezoids. Learn their properties, angle relationships, and area formulas.

Geometry

Beginner

~45 min

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1. What is a Quadrilateral?

A quadrilateral is a polygon with exactly 4 sides, 4 vertices, and 4 interior angles.

Angle Sum Property

\angle A + \angle B + \angle C + \angle D = 360°

The sum of interior angles in any quadrilateral is always 360°.

Convex Quadrilateral

All interior angles < 180°. All vertices point outward.

Concave Quadrilateral

One interior angle > 180°. Has an "inward dent".

2. Parallelogram

A parallelogram has two pairs of parallel sides.

Properties

Opposite sides are equal and parallel
Opposite angles are equal
Consecutive angles are supplementary (180°)
Diagonals bisect each other

Formulas

Area:

A = b \times h

Perimeter:

P = 2(a + b)

3. Rectangle

A rectangle is a parallelogram with all angles = 90°.

Properties

All parallelogram properties
All four angles are 90°
Diagonals are equal in length

Formulas

A = l \times w

P = 2(l + w)

d = \sqrt{l^2 + w^2}

4. Rhombus

A rhombus is a parallelogram with all sides equal.

Properties

All parallelogram properties
All four sides are equal
Diagonals are perpendicular
Diagonals bisect the vertex angles

Formulas

A = \frac{1}{2}d_1 \times d_2

P = 4s

5. Square

A square is a rectangle with all sides equal (or a rhombus with all angles 90°).

The Square is Special!

A square has ALL properties of rectangles AND rhombi.

A = s^2

Area

P = 4s

Perimeter

d = s\sqrt{2}

Diagonal

6. Trapezoid

A trapezoid has exactly one pair of parallel sides (called bases).

Properties

One pair of parallel sides (bases)
The non-parallel sides are called legs
Isosceles trapezoid: legs are equal

Area Formula

A = \frac{1}{2}(a + b) \times h

a, b = parallel sides; h = height

Practice Quiz

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