We will discuss all types of quadrilaterals except the concave quadrilateral. (See diagram).
This type of quadrilateral has one angle greater than 180°. (Angles greater than 180° are called concave angles). These quadrilaterals
are not discussed much in a typical geometry course and are not among the quadrilaterals with which you are familiar.
Generally, all a quadrilateral needs to be classified as such is four sides. However, there are six specific quadrilaterals that are worth discussing
in detail.

We will discuss all types of quadrilaterals except the concave quadrilateral. (See diagram).

This type of quadrilateral has one angle greater than 180°. (Angles greater than 180° are called concave angles). These quadrilaterals are not discussed much in a typical geometry course and are not among the quadrilaterals with which you are familiar.

Generally, all a quadrilateral needs to be classified as such is four sides. However, there are six specific quadrilaterals that are worth discussing in detail.

Click here for a trapezoid calculator.

The British use the term trapezoid to refer to a quadrilateral with no parallel sides and a trapezium is a quadrilateral with two parallel sides.

The American usage is the exact opposite of the British usage: trapezoid –
two parallel sides trapezium – no parallel sides.
The only requirement for a trapezoid (American definition) is that two sides are parallel.
The non-parallel sides (side b and side d) are called legs.
Lines AC and BD are the diagonals.
The median is perpendicular to the height and bisects lines AB and CD.
∠ A plus ∠ B = 180° ∠ C plus ∠ D = 180°
Trapezoid Area = ½ • (sum of the parallel sides) • height
height² = [(a +b -c +d) • (-a +b +c +d) • (a -b -c +d) • (a +b -c -d)] ÷ (4 • (a -c)²)
The legs and diagonals of an isosceles trapezoid are equal.
Both pairs of base angles are equal
The right trapezoid has two right angles.

The only requirement for a trapezoid (American definition) is that two sides are parallel.

The non-parallel sides (side b and side d) are called legs.
Lines AC and BD are the diagonals.
The median is perpendicular to the height and bisects lines AB and CD.
∠ A plus ∠ B = 180° ∠ C plus ∠ D = 180°
Trapezoid Area = ½ • (sum of the parallel sides) • height
height² = [(a +b -c +d) • (-a +b +c +d) • (a -b -c +d) • (a +b -c -d)] ÷ (4 • (a -c)²)
The legs and diagonals of an isosceles trapezoid are equal.
Both pairs of base angles are equal
The right trapezoid has two right angles.

Lines AC and BD are the diagonals.
The median is perpendicular to the height and bisects lines AB and CD.
∠ A plus ∠ B = 180° ∠ C plus ∠ D = 180°
Trapezoid Area = ½ • (sum of the parallel sides) • height
height² = [(a +b -c +d) • (-a +b +c +d) • (a -b -c +d) • (a +b -c -d)] ÷ (4 • (a -c)²)
The legs and diagonals of an isosceles trapezoid are equal.
Both pairs of base angles are equal
The right trapezoid has two right angles.

The median is perpendicular to the height and bisects lines AB and CD.
∠ A plus ∠ B = 180° ∠ C plus ∠ D = 180°
Trapezoid Area = ½ • (sum of the parallel sides) • height
height² = [(a +b -c +d) • (-a +b +c +d) • (a -b -c +d) • (a +b -c -d)] ÷ (4 • (a -c)²)
The legs and diagonals of an isosceles trapezoid are equal.
Both pairs of base angles are equal
The right trapezoid has two right angles.

∠ A plus ∠ B = 180° ∠ C plus ∠ D = 180°

Trapezoid Area = ½ • (sum of the parallel sides) • height

height² = [(a +b -c +d) • (-a +b +c +d) • (a -b -c +d) • (a +b -c -d)] ÷ (4 • (a -c)²)

The legs and diagonals of an isosceles trapezoid are equal.
Both pairs of base angles are equal
The right trapezoid has two right angles.

Both pairs of base angles are equal

The right trapezoid has two right angles.

Click here for a kite calculator.

∠ B = ∠ C and are the non-vertex angles
Lines AD and BC are diagonals and always meet at right angles.
Diagonal AD is the axis of symmetry and bisects diagonal BC, bisects ∠ A and ∠ D,
and bisects the kite into two congruent, triangles. (△ ABD and △ ACD)
Diagonal BC bisects the kite into two isosceles triangles. (△ ABC and △ BCD)
Side AB = side AC, side BD = side CD and Line OB = Line OC

∠ B = ∠ C and are the non-vertex angles
Lines AD and BC are diagonals and always meet at right angles.
Diagonal AD is the axis of symmetry and bisects diagonal BC, bisects ∠ A and ∠ D,
and bisects the kite into two congruent, triangles. (△ ABD and △ ACD)
Diagonal BC bisects the kite into two isosceles triangles. (△ ABC and △ BCD)
Side AB = side AC, side BD = side CD and Line OB = Line OC

Lines AD and BC are diagonals and always meet at right angles.
Diagonal AD is the axis of symmetry and bisects diagonal BC, bisects ∠ A and ∠ D,
and bisects the kite into two congruent, triangles. (△ ABD and △ ACD)
Diagonal BC bisects the kite into two isosceles triangles. (△ ABC and △ BCD)
Side AB = side AC, side BD = side CD and Line OB = Line OC

Diagonal AD is the axis of symmetry and bisects diagonal BC, bisects ∠ A and ∠ D,
and bisects the kite into two congruent, triangles. (△ ABD and △ ACD)
Diagonal BC bisects the kite into two isosceles triangles. (△ ABC and △ BCD)
Side AB = side AC, side BD = side CD and Line OB = Line OC

Diagonal BC bisects the kite into two isosceles triangles. (△ ABC and △ BCD)

Side AB = side AC, side BD = side CD and Line OB = Line OC

Click here for a parallelogram calculator.

Click here for a rhombus calculator.

Click here for a rectangle and square calculator.

All 4 angles are right angles

Diagonals bisect each other and are equal

Rectangle Area = length × width

Perimeter = (2 × length) + (2 × width)

Click here for a rectangle and square calculator.

All 4 angles are right angles

Diagonals bisect each other at right angles and are equal

Perimeter = 4 × side length

Area = (side length)2

A circle can be circumscribed around a cyclic quadrilateral and its opposite angles add up to 180°

A circle can be inscribed inside a tangential quadrilateral.

You are watching: QUADRILATERALS. Info created by GBee English Center selection and synthesis along with other related topics.