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Lesson: Special Quadrilaterals
Contributed by: Pappal
There are three special types of quadrilaterals
Parallelograms
There are three special types of quadrilaterals
Parallelograms
There are three special types of quadrilaterals
Parallelograms
There are three special types of quadrilaterals
Trapezoids
Parallelograms
There are three special types of quadrilaterals
Trapezoids
Parallelograms
There are three special types of quadrilaterals
Trapezoid
Kites
Parallelograms
There are three special types of quadrilaterals
Trapezoid
Kites
Parallelograms
?
Trapezoid
?
Kites
?
A trapezoid is a quadrilateral
A trapezoid is a quadrilateral
which has only two sides parallel
A trapezoid is a quadrilateral
which has only two sides parallel
A trapezoid is a quadrilateral
which has only two sides parallel
A trapezoid is a quadrilateral
which has only two sides parallel
A trapezoid is a quadrilateral
which has only two sides parallel
Is this a trapezoid?
yes
?
no
?
A trapezoid has a couple special properties.
A trapezoid has a couple special properties.
because a pair of lines are parallel
A trapezoid has a couple special properties.
because a pair of lines are parallel
A trapezoid has a couple special properties.
same side interior angles (bracket) add to 180
because a pair of lines are parallel
A trapezoid has a couple special properties.
same side interior angles (bracket) add to 180
because a pair of lines are parallel
A trapezoid has a couple special properties.
same side interior angles (bracket) add to 180
because a pair of lines are parallel
70
The median of a trapezoid
The median of a trapezoid
connects the two midpoints of the NON-PARALLEL
sides
midpoint
The median of a trapezoid
connects the two midpoints of the NON-PARALLEL
sides
The median of a trapezoid
connects the two midpoints of the NON-PARALLEL
midpoint
sides
The median of a trapezoid
connects the two midpoints of the NON-PARALLEL
median
sides
The median of a trapezoid
The median of a trapezoid can also be called the
connects the two midpoints of the NON-PARALLEL
midsegment
sides
Median of a trapezoid is also called
Mean
Midsegment
Mode
Middle Earth
The median is parallel to the other two sides
The median is parallel to the other two sides
The median is parallel to the other two sides
and is the average of those two sides
The median is parallel to the other two sides
and is the average of those two sides
5
The median is parallel to the other two sides
and is the average of those to sides
5
9
The median is parallel to the other two sides
and is the average of those to sides
5
5
9
The median is parallel to the other two sides
and is the average of those to sides
5 +
5
9
The median is parallel to the other two sides
and is the average of those to sides
5 + 9
5
9
The median is parallel to the other two sides
and is the average of those to sides
5 + 9 = 14
5
9
The median is parallel to the other two sides
and is the average of those to sides
5 + 9 = 14 ÷
5
9
The median is parallel to the other two sides
and is the average of those to sides
5 + 9 = 14 ÷ 2
5
9
The median is parallel to the other two sides
and is the average of those to sides
5 + 9 = 14 ÷ 2 = 7
5
9
The median is parallel to the other two sides
and is the average of those to sides
5 + 9 = 14 ÷ 2 = 7
5
9
7
8
12
An isosceles trapezoid is a special trapezoid
An isosceles trapezoid is a special trapezoid
An isosceles trapezoid is a special trapezoid
where the NON-PARALLEL sides are equal
An isosceles trapezoid is a special trapezoid
where the NON-PARALLEL sides are equal
Isosceles Trapezoid has which sides equal
Parallel sides
Non-parallel sides
In an isosceles trapezoid
In an isosceles trapezoid
In an isosceles trapezoid
the base angles are congruent
In an isosceles trapezoid
the base angles are congruent
In an isosceles trapezoid
the base angles are congruent
70
110
Also, in an isosceles trapezoid
Also, in an isosceles trapezoid
Also, in an isosceles trapezoid
the diagonals are congruent
Also, in an isosceles trapezoid
the diagonals are congruent
C
A
Also, in an isosceles trapezoid
the diagonals are congruent
C
D
A
B
Also, in an isosceles trapezoid
the diagonals are congruent
C
D
AC ≅ BD
A
B
C
AC = x + 5
BD = 15
D
A
x =
B
The other special quadrilateral is the kite
The other special quadrilateral is the kite
The other special quadrilateral is the kite
which has two pairs of adjacent
sides congruent
The other special quadrilateral is the kite
which has two pairs of adjacent
sides congruent
The other special quadrilateral is the kite
which has two pairs of adjacent
sides congruent
13
5
Kites have several special properties
Kites have several special properties
Kites have several special properties
the 'wing' angles are congruent
Kites have several special properties
the 'wing' angles are congruent
110
Kites have several special properties
the 'wing' angles are congruent
the diagonal bisects the 
non-'wing' angles
Kites have several special properties
the 'wing' angles are congruent
the diagonal bisects the 
non-'wing' angles
Kites have several special properties
the 'wing' angles are congruent
the diagonal bisects the 
non-'wing' angles
Kites have several special properties
the 'wing' angles are congruent
the diagonal bisects the 
non-'wing' angles
1
A
2
Angle 2 =
Angle A = 80ο
Angle 1 =
ο
ο
Kites have several special properties
the 'wing' angles are congruent
the diagonal bisects the 
non-'wing' angles
this diagonal also bisects the
other diagonal
Kites have several special properties
the 'wing' angles are congruent
the diagonal bisects the 
non-'wing' angles
this diagonal also bisects the
other diagonal
Kites have several special properties
the 'wing' angles are congruent
the diagonal bisects the 
non-'wing' angles
this diagonal also bisects the
other diagonal
B
E
D
BD = 8
ED =
BE =
Kites have several special properties
the 'wing' angles are congruent
the diagonal bisects the 
non-'wing' angles
this diagonal also bisects the
other diagonal
the diagonals are
perpendicular
Kites have several special properties
the 'wing' angles are congruent
the diagonal bisects the 
non-'wing' angles
this diagonal also bisects the
other diagonal
the diagonals are
perpendicular
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