1. Dapo Adegbile Brandon Abad Jude St. Jean Period:12
Trapezoids
Dapo Adegbile
Brandon Abad
Jude St. Jean Period:12

2. Definition A quadrilateral that has 1 pair of parallel sides
A trapezoid with 1 pair of congruent sides

3. 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. 

4. 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.

5. Proof Given: BC ll AD, AB = DC Prove: <1=<2 Given
Construction
Definition of a parallelogram
Opposite sides of Parallelogram are congruent
Transitive Property
Isosceles Triangle Theorem (if sides than angles)
Corresponding angles
Transitive property
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

6. Properties of diagonals
The diagonals of an isosceles triangle are congruent.
Nothing special happens with the diagonals.

7. Proof Given Quad. PQRS is a trapezoid SR ll PQ SP=RQ
Given: PQRS is an Isosceles Trapezoid
SR ll PQ SP=RQ
Prove: RP=SQ
Given
Definition of Trapezoid
Reflexive Property
CPCTC
Quad. PQRS is a trapezoid
SR ll PQ
SP=RQ
<SPQ=<RPQ
PQ=PQ
RP=SQ

8. Lines of symmetry A regular trapezoid has no lines of symmetry
Isosceles trapezoids have only 1 line of symmetry

9. Coordinate Geometry

10. 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

11. Other facts 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

12. Suggested Websites http://mathopenref.com/coordtrapezoid.html