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Classifying Quadrilaterals
Only ODD
Lesson 6.15
Quadrilaterals
Objectives
• To identify any quadrilateral, by name, as
specifically as you can, based on its
characteristics
Quadrilateral
• a quadrilateral is a polygon with 4 sides.
Specific Quadrilaterals
• There are several specific types of
quadrilaterals. They are classified based
on their sides or angles.
Quadrilaterals
2 pairs adjacent
congruent sides
1 pair parallel sides
2 pairs parallel
sides
Trapezoid
Parallelogram
non-parallel sides
are congruent
4 congruent sides
4 right angles
Kite
Isosceles
Trapezoid
Rhombus
Rectangle
Square
Quadrilaterals
2 pairs adjacent
congruent sides
1 pair parallel sides
A quadrilateral
simply has 4 sides –
no other special
requirements.
2 pairs parallel
sides
Trapezoid
Parallelogram
non-parallel sides
are congruent
4 congruent sides
4 right angles
Kite
Isosceles
Trapezoid
Rhombus
Rectangle
Square
Examples of Quadrilaterals
A parallelogram
has two pairs of
parallel sides.
Quadrilaterals
2 pairs adjacent
congruent sides
1 pair parallel sides
2 pairs parallel
sides
Trapezoid
Parallelogram
non-parallel sides
are congruent
4 congruent sides
4 right angles
Kite
Isosceles
Trapezoid
Rhombus
Rectangle
Square
Parallelogram
• Two pairs of parallel sides
• opposite sides are actually congruent.
Parallelogram
In a parallelogram opposite sides are equal and parallel.
The diagonals of a parallelogram bisect each other.
A parallelogram has rotational symmetry of order 2.
Quadrilaterals
2 pairs adjacent
congruent sides
1 pair parallel sides
2 pairs parallel
sides
Trapezoid
Parallelogram
non-parallel sides
are congruent
4 congruent sides
4 right angles
Kite
Isosceles
Trapezoid
Rhombus
Rectangle
A rhombus is a parallelogram
that has four congruent sides.
Square
Rhombus
• Still has two pairs of parallel sides; with
opposite sides congruent.
4 in.
4 in.
4 in.
4 in.
Rhombus
A rhombus is a parallelogram with four equal sides.
The diagonals of a rhombus bisect each other at right angles.
A rhombus has two lines of symmetry and it has rotational
symmetry of order 2.
Quadrilaterals
2 pairs adjacent
congruent sides
1 pair parallel sides
2 pairs parallel
sides
Trapezoid
Parallelogram
non-parallel sides
are congruent
4 congruent sides
4 right angles
Kite
Isosceles
Trapezoid
Rhombus
Rectangle
A rectangle has
four right angles.
Square
Rectangle
• Still has two pairs of parallel sides; with
opposite sides congruent.
• Has four right angles
Rectangle
A rectangle has opposite sides of equal length and four
right angles.
A rectangle has two lines of symmetry.
Quadrilaterals
2 pairs adjacent
congruent sides
1 pair parallel sides
2 pairs parallel
sides
Trapezoid
Parallelogram
4 congruent sides
non-parallel sides
are congruent
4 right angles
Kite
Isosceles
Trapezoid
Rhombus
Rectangle
A square is a specific case of both a
rhombus AND a rectangle, having four
right angles and 4 congruent sides.
Square
Square
• Still has two pairs of parallel sides.
• Has four congruent sides
• Has four right angles
Square
A square has four equal sides and four right angles.
It has four lines of symmetry and rotational symmetry of
order 4.
A trapezoid has
only one pair of
parallel sides.
2 pairs adjacent
congruent sides
Quadrilaterals
1 pair parallel sides
2 pairs parallel
sides
Trapezoid
Parallelogram
non-parallel sides
are congruent
4 congruent sides
4 right angles
Kite
Isosceles
Trapezoid
Rhombus
Rectangle
Square
An isosceles
trapezoid is a
trapeziod with the
non-parallel sides
2 pairs adjacent
congruent. congruent sides
Quadrilaterals
1 pair parallel sides
2 pairs parallel
sides
Trapezoid
Parallelogram
non-parallel sides
are congruent
4 congruent sides
4 right angles
Kite
Isosceles
Trapezoid
Rhombus
Rectangle
Square
Trapezoid
• has one pair of parallel sides.
trapezoids
Isosceles trapezoid
(Each of these examples shown has top and bottom sides parallel.)
Trapezium
A trapezium has one pair of opposite sides that are
parallel.
Can a trapezium have any lines of symmetry?
Can a trapezium have rotational symmetry?
Isosceles trapezium
In an isosceles trapezium the two opposite non-parallel
sides are the same length.
The diagonals of an isosceles trapezium are the same length.
It has one line of symmetry.
Quadrilaterals
2 pairs adjacent
congruent sides
1 pair parallel sides
2 pairs parallel
sides
Trapezoid
Parallelogram
non-parallel sides
are congruent
4 congruent sides
4 right angles
Kite
An kite is a quadrilateral
with NO parallel sides but 2
pairs of adjacent congruent
sides.
Isosceles
Trapezoid
Rhombus
Rectangle
Square
Example of a Kite
4 in.
4 in.
2 in.
2 in.
Kite
A kite has two pairs of adjacent sides of equal length.
The diagonals of a kite cross at right angles.
A kite has one line of symmetry.
Special Quadrilaterals
A parallelogram is a quadrilateral with both pairs
of opposite sides parallel.
A rhombus is a parallelogram with four
congruent sides.
A rectangle is a parallelogram with four right
angles.
A square is a parallelogram with four congruent
sides and right angles.
A kite is a quadrilateral with two pairs of adjacent
sides congruent and no opposite sides congruent.
A trapezoid is a quadrilateral with exactly one
pair of parallel sides. The isosceles trapezoid at
the right is a trapezoid whose nonparallel sides
(legs) are congruent.
Quadrilateral
Parallelogram
Rectangle
Rhombus
Square
Trapezoid
What are all of the names for this polygon?
Quadrilateral
 Parallelogram
 Rectangle
Which name best describes the shape?
What are all of the names for this polygon?
Quadrilateral
 Parallelogram
Which name best describes the shape?
What are all of the names for this polygon?
Quadrilateral
 Parallelogram
 Rhombus
Which name best describes the shape?
What are all of the names for this polygon?
Quadrilateral
 Trapezoid
Which name best describes the shape?
What are all of the names for this polygon?
Quadrilateral
 Parallelogram
 Square
Rhombus
Rectangle
Which name best describes the shape?
Using Properties
• Find the value of the variables for the kite:
T
x+6
2y + 5
J
K
3x - 5
2x + 4
B
JB = KB
2x + 4 = 3x – 5
-x = -9
x=9
TK = 9 + 6
TK = 15
TJ => 2y + 5 = 15
2y = 10
y=5
Using Properties
• Find the values of the variables for the
rhombus:
3b + 2
5a + 4
3b + 2 = 4b -2
b=4
3a + 8
4b - 2
5a + 4 = 3a + 8
2a = 4
a=2
Lesson Quiz
Complete each statement.
1. A quadrilateral with four right angles is a
_________.
square or rectangle
2. A parallelogram with four right angles and four
congruent sides is a _______. square
3. A figure with 4 sides and 4 angles is a ______.
quadrilateral
4. Give the most descriptive name for this
quadrilateral.
trapezoid
1
2
3
4
Interior Angles
• Interior angles: An interior angle (or
internal angle) is an angle formed by two
sides of a simple polygon that share an
endpoint
• Interior angles of a quadrilateral always
equal 360 degrees