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Trapezoids
Jude Saint-Jean
Dapo
Brandon
Period:12
Definition

A quadrilateral which
has at least 1 pair of
parallel sides

A trapezoid with 1 pair
of congruent sides
Properties of sides


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The bases (top and bottom) of an
isosceles trapezoid are parallel.
Opposite sides 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.
That's it. No sides needs to be
congruent and no angles need to be
congruent.
Properties of angles

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Adjacent angles along
the sides are
supplementary.
Base angles of isosceles
trapezoid are
congruent.
Normal trapezoids
don’t have any special
properties.
Proof
Given: <a=102 & <d is adjacent
to <a & it’s an isosceles
trapezoid
<a = 102


Prove: <d is supp. to <a
Given
Same side interior angles
<a is congruent to <b
Angle property of quadrilateral(1,2)
<a+<b+<c+<d = 360
Same side interior angles(3)
<c is congruent to <d
Addition property(4)
<d is supp. to <a
Properties of diagonals

The diagonals (not
show here) are
congruent.

Nothing special
happens with the
diagonals.
Lines of symmetry

A regular trapezoid has no lines of
symmetry

Isosceles trapezoids have only 1 line
of symmetry
formulas

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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.
Other facts

Altitude: The altitude of a trapezoid is
the perpendicular distance from one base to the
other. (One base may need to be extended).

Median: The median of a trapezoid is a line
joining the midpoints of the two legs.
Connection to coordinate geometry


Trapezoid and its properties. (Coordinate
Geometry)
Trapezoid area and perimeter.
(Coordinate Geometry)
Websites
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Mathopenref.com
Coolmath.com