TrapezoidsTrapezoids

Dapo AdegbileDapo Adegbile

Brandon AbadBrandon Abad

Jude St. JeanJude St. JeanPeriod:12Period:12

DefinitionDefinition

A quadrilateral that has A quadrilateral that has 1 pair of parallel sides1 pair of parallel sides

A trapezoid with 1 pair A trapezoid with 1 pair of congruent sidesof congruent sides

Properties of sidesProperties of sides The bases (top and bottom) of an The bases (top and bottom) of an

isosceles trapezoid are parallel.isosceles trapezoid are parallel. The legs of an isosceles trapezoid The legs of an isosceles trapezoid

are congruent.are congruent. The angles on either side of the The angles on either side of the

bases are congruent.bases are congruent.

The bases (top and bottom) of a The bases (top and bottom) of a trapezoid are parallel.trapezoid are parallel.

Unlike the Isosceles Trapezoid it Unlike the Isosceles Trapezoid it does not need to have any does not need to have any congruent sides. congruent sides. 

Properties of anglesProperties of angles Adjacent angles along the Adjacent angles along the

sides are supplementary.sides are supplementary. Base angles of isosceles Base angles of isosceles

trapezoid are congruent.trapezoid are congruent. Normal trapezoids don’t Normal trapezoids don’t

have any special have any special properties.properties.

All of the angles within a All of the angles within a trapezoid add up to 360 trapezoid add up to 360 degrees.degrees.

1.1. GivenGiven

2.2. GivenGiven

3.3. GivenGiven

4.4. ConstructionConstruction

5.5. ConstructionConstruction

6.6. Definition of a parallelogramDefinition of a parallelogram

7.7. Opposite sides of Parallelogram are Opposite sides of Parallelogram are congruentcongruent

8.8. Transitive PropertyTransitive Property

9.9. Isosceles Triangle Theorem (if sides Isosceles Triangle Theorem (if sides than angles)than angles)

10.10. Corresponding anglesCorresponding angles

11.11. Transitive propertyTransitive property

ProofProof

1.1. Quad. ABCD is an Isosceles Quad. ABCD is an Isosceles TrapezoidTrapezoid

2.2. BC ll ADBC ll AD

3.3. AB = DCAB = DC

4.4. Construct a line through C that Construct a line through C that is ll to ABis ll to AB

5.5. AB ll ECAB ll EC

6.6. Quad ABCE is a parallelogramQuad ABCE is a parallelogram

7.7. AB = ECAB = EC

8.8. DC = CEDC = CE

9.9. <3 = <4<3 = <4

10.10. <1 = <3<1 = <3

11.11. <1 = <4<1 = <4

Given: BC ll AD, AB = DC

Prove: <1=<2

Properties of diagonalsProperties of diagonals

The diagonals of an The diagonals of an isosceles triangle are isosceles triangle are congruent.congruent.

Nothing special Nothing special happens with the happens with the diagonalsdiagonals..

ProofProof

1.1. Quad. PQRS is a Quad. PQRS is a trapezoidtrapezoid

2.2. SR ll PQSR ll PQ3.3. SP=RQSP=RQ4.4. <SPQ=<RPQ<SPQ=<RPQ5.5. PQ=PQPQ=PQ6.6. RP=SQRP=SQ

1.1. GivenGiven

2.2. GivenGiven

3.3. GivenGiven

4.4. Definition of TrapezoidDefinition of Trapezoid

5.5. Reflexive PropertyReflexive Property

6.6. CPCTCCPCTC

Given: PQRS is an Isosceles Trapezoid

SR ll PQ SP=RQ

Prove: RP=SQ

Lines of symmetryLines of symmetry

A regular trapezoid has no lines of A regular trapezoid has no lines of symmetrysymmetry

Isosceles trapezoids have only 1 line Isosceles trapezoids have only 1 line of symmetryof symmetry

Coordinate GeometryCoordinate Geometry

http://mathopenref.com/coordtrapezoid.htmlhttp://mathopenref.com/coordtrapezoid.html

formulasformulas Perimeter = a + b + c +Perimeter = a + b + c +

 B B

Area = 1/2h(B+b)Area = 1/2h(B+b)       Area of parallelogram Area of parallelogram

(B+b) x h  (B+b) x h   But, this is double of But, this is double of

what we need. So, multiply what we need. So, multiply by 1/2.by 1/2.

The Area could also be The Area could also be altitude x medianaltitude x median

Other factsOther facts Right Trapezoid- a trapezoid with 2 right anglesRight Trapezoid- a trapezoid with 2 right angles medianmedian- is a line segment linking the midpoints of the two legs - is a line segment linking the midpoints of the two legs

of the trapezoidof the trapezoid To find the length of the median you can find the length To find the length of the median you can find the length

of the base and divide it by 2 or find the distance of the base and divide it by 2 or find the distance between the 2 midpoints of the legs between the 2 midpoints of the legs

AltitudeAltitude- is the - is the perpendicularperpendicular distance from one base to the distance from one base to the otherother

British call it TrapeziumBritish call it Trapezium

Suggested WebsitesSuggested Websites

http://mathopenref.com/coordtrapezoihttp://mathopenref.com/coordtrapezoid.htmld.html

http://www.coolmath.com/reference/trhttp://www.coolmath.com/reference/trapezoids.htmlapezoids.html

http://www.cliffsnotes.com/http://www.cliffsnotes.com/study_guide/Properties-of-study_guide/Properties-of-Trapezoids.topicArticleId-Trapezoids.topicArticleId-18851,articleId-18798.html18851,articleId-18798.html