Transcript Trapezoids - BowerPower.net

Trapezoids
Geometry
Chapter 6
A BowerPoint Presentation
Definition of trapezoid
A trapezoid is a quadrilateral with EXACTLY
ONE pair of parallel sides.
Definition of trapezoid
A trapezoid is a quadrilateral with EXACTLY
ONE pair of parallel sides.
Parts of a trapezoid
The parallel sides of the trapezoid are called
bases.
BASES
Parts of a trapezoid
The non-parallel sides of the trapezoid are
called legs.
LEGS
Parts of a trapezoid
There are two pairs of base angles.
Parts of a trapezoid
There are two pairs of base angles.
BASE ANGLES (1st Pair)
Parts of a trapezoid
There are two pairs of base angles.
BASE ANGLES (1st Pair)
BASE ANGLES (2nd Pair)
Identify bases & legs
What segments are the
bases?
What segments are the
legs?
Identify bases & legs
What segments are the
bases?
WX & YZ
What segments are the
legs?
XY & WZ
Geometry violence
If you think about it, a trapezoid is a
triangle…
Geometry violence
If you think about it, a trapezoid is a
triangle…that got its top chopped off!!!
Geometry violence
If you think about it, a trapezoid is a
triangle…that got its top chopped off!!!
Geometry violence
If you think about it, a trapezoid is a
triangle…that got its top chopped off!!!
Geometry violence
If you think about it, a trapezoid is a
triangle…that got its top chopped off!!!
Geometry violence
If you think about it, a trapezoid is a
triangle…that got its top chopped off!!!
Trapezoids & triangles
As a result, it is not surprising that
trapezoids & triangles have some
similarities.
Trapezoids & triangles
As a result, it is not surprising that
trapezoids & triangles have some
similarities.
What do you call a triangle with
2
sides?
Trapezoids & triangles
As a result, it is not surprising that
trapezoids & triangles have some
similarities.
What do you call a triangle with
2
sides?
What are the
sides called?
Isosceles trapezoid
An isosceles trapezoid has
one pair of
sides.
Isosceles trapezoid
An isosceles trapezoid has
one pair of
sides.
(Only legs can be
. Why?)
Isosceles triangles & trapezoids
In isosceles triangle ABC,
B is a vertex
.
What are
A &
C called?
Isosceles triangles & trapezoids
What do you know about
A &
C ?
If isosceles trapezoid, then each
pair of base
s
If isosceles trapezoid, then each
pair of base
s
If isosceles trapezoid, then each
pair of base
s
If one pair of base s
in a
trapezoid, then isosceles trapezoid
If one pair of base s
in a
trapezoid, then isosceles trapezoid
Trapezoid is isosceles IF AND
ONLY IF diagonals congruent
Trapezoid is isosceles IF AND
ONLY IF diagonals congruent
If WY
XZ
then WXYZ is
isosceles trapezoid
Trapezoid is isosceles IF AND
ONLY IF diagonals congruent
If WY
XZ
then WXYZ is
isosceles trapezoid
Think about it…
It is possible for WY
XZ.
Can WY and XZ bisect each other?
Midsegment of a triangle
Remember that the midsegment of a triangle
connects the midpoints of two sides.
Midsegment of a triangle
Remember that the midsegment of a triangle
connects the midpoints of two sides.
Midsegment of a triangle
It is always parallel to the third side.
Midsegment of a triangle
Do you remember the relationship between
the length of the third side and the length
of the midsegment?
Midsegment of a triangle
Do you remember the relationship between
the length of the third side and the length
of the midsegment?
What is the value of x?
x
30
Midsegment of a triangle
Do you remember the relationship between
the length of the third side and the length
of the midsegment?
What is the value of x?
(x = 15)
x
30
Midsegment of a triangle
Do you remember the relationship between
the length of the third side and the length
of the midsegment?
What is the value of x?
20
x
Midsegment of a triangle
Do you remember the relationship between
the length of the third side and the length
of the midsegment?
What is the value of x?
(x = 40)
20
x
Midsegment of a triangle
(Length of 3rd side)
or
2 (Midsegment) = Length of 3rd side
Midsegment =
9
18
Midsegment of a trapezoid
The midsegment of a trapezoid connects the
midpoints of the two legs
Trapezoid Midsegment Theorem
Two things happen in the Trapezoid
Midsegment Theorem…
Trapezoid Midsegment Theorem
#1 – The midsegment is parallel to both
bases
Trapezoid Midsegment Theorem
#1 – The midsegment is parallel to both
bases
Trapezoid Midsegment Theorem
#2 – The length of the midsegment equals
the average length of the bases
Trapezoid Midsegment Theorem
#2 – The length of the midsegment equals
the average length of the bases
8
x
16
Trapezoid Midsegment Theorem
#2 – The length of the midsegment equals
the average length of the bases
8
x = 12
16
Trapezoid Midsegment Theorem
Trapezoid Midsegment Theorem
Solve for x
27
x
45
Trapezoid Midsegment Theorem
Solve for x
27
x
45
(x = 36)
Trapezoid Midsegment Theorem
Solve for x
11
24
x
Trapezoid Midsegment Theorem
Solve for x
11
24
x
(x = 37)