Download The bases (top and bottom) of an isosceles trapezoid

Trapezoids
Dapo Adegbile
Brandon Abad
Jude St. Jean
Period:12
Definition

A quadrilateral that has
1 pair of parallel sides

A trapezoid with 1 pair
of congruent sides
Properties of sides





The bases (top and bottom) of an
isosceles trapezoid are parallel.
The legs of an isosceles trapezoid
are congruent.
The angles on either side of the
bases are congruent.
The bases (top and bottom) of a
trapezoid are parallel.
Unlike the Isosceles Trapezoid it
does not need to have any
congruent sides.
Properties of angles




Adjacent angles along the
sides are supplementary.
Base angles of isosceles
trapezoid are congruent.
Normal trapezoids don’t
have any special
properties.
All of the angles within a
trapezoid add up to 360
degrees.
Proof
Given: BC ll AD, AB = DC
Prove: <1=<2
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Quad. ABCD is an Isosceles
Trapezoid
BC ll AD
AB = DC
Construct a line through C that
is ll to AB
AB ll EC
Quad ABCE is a parallelogram
AB = EC
DC = CE
<3 = <4
<1 = <3
<1 = <4
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Given
Given
Given
Construction
Construction
Definition of a parallelogram
Opposite sides of Parallelogram are
congruent
Transitive Property
Isosceles Triangle Theorem (if sides
than angles)
Corresponding angles
Transitive property
Properties of diagonals

The diagonals of an
isosceles triangle are
congruent.

Nothing special
happens with the
diagonals.
Proof
Given: PQRS is an Isosceles Trapezoid
SR ll PQ
SP=RQ
Prove: RP=SQ
1.
2.
3.
4.
5.
6.
Quad. PQRS is a
trapezoid
SR ll PQ
SP=RQ
<SPQ=<RPQ
PQ=PQ
RP=SQ
1.
2.
3.
4.
5.
6.
Given
Given
Given
Definition of Trapezoid
Reflexive Property
CPCTC
Lines of symmetry

A regular trapezoid has no lines of
symmetry

Isosceles trapezoids have only 1 line
of symmetry
Coordinate Geometry

http://mathopenref.com/coordtrapezoid.html
formulas

Perimeter = a + b + c +
B

Area = 1/2h(B+b)
Area of parallelogram
(B+b) x h
But, this is double of
what we need. So, multiply
by 1/2.
The Area could also be
altitude x median


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Other facts



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Right Trapezoid- a trapezoid with 2 right angles
median- is a line segment linking the midpoints of the two legs
of the trapezoid
 To find the length of the median you can find the length
of the base and divide it by 2 or find the distance
between the 2 midpoints of the legs
Altitude- is the perpendicular distance from one base to the
other
British call it Trapezium
Suggested Websites
http://mathopenref.com/coordtrapezoi
d.html
http://www.coolmath.com/reference/tr
apezoids.html
http://www.cliffsnotes.com/study_guid
e/Properties-ofTrapezoids.topicArticleId18851,articleId-18798.html