TrapezoidsTrapezoids

Jude Saint-JeanJude Saint-Jean

DapoDapo

BrandonBrandon

Period:12Period:12

DefinitionDefinition

A quadrilateral which A quadrilateral which has at least 1 pair of has at least 1 pair of parallel sidesparallel 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. Opposite sides of an isosceles Opposite sides of an isosceles

trapezoid are congruent.trapezoid 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.

That's it.  No sides needs to be That's it.  No sides needs to be congruent and no angles need to be congruent and no angles need to be congruent. congruent. 

Properties of anglesProperties of angles

Adjacent angles along Adjacent angles along the sides are the sides are supplementary.supplementary.

Base angles of isosceles Base angles of isosceles trapezoid are trapezoid are congruent.congruent.

Normal trapezoids Normal trapezoids don’t have any special don’t have any special properties.properties.

ProofProof

Given: <a=102 & <d is adjacent Given: <a=102 & <d is adjacent to <a & it’s an isosceles to <a & it’s an isosceles trapezoidtrapezoid

<a = 102<a = 102

<a is congruent to <b<a is congruent to <b

<a+<b+<c+<d = 360<a+<b+<c+<d = 360

<c is congruent to <d<c is congruent to <d

<d is supp. to <a<d is supp. to <a

Prove: <d is supp. to <aProve: <d is supp. to <a

GivenGiven

Same side interior anglesSame side interior angles

Angle property of quadrilateral(1,2)Angle property of quadrilateral(1,2)

Same side interior angles(3)Same side interior angles(3)

Addition property(4)Addition property(4)

Properties of diagonalsProperties of diagonals

The diagonals (not The diagonals (not show here) are show here) are congruent.congruent.

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

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

formulasformulas Perimeter = a + b + c + BPerimeter = a + b + c + B

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

But, this is double of what we But, this is double of what we need...  So, multiply by 1/2.need...  So, multiply by 1/2.

Other factsOther facts

Altitude: Altitude: The The altitudealtitude of a trapezoid is the  of a trapezoid is the perpendicularperpendicular distance from one base to the  distance from one base to the other. (One base may need to be extended).other. (One base may need to be extended).

Median: Median: The median of a trapezoid is a line The median of a trapezoid is a line joining the midpoints of the two legs. joining the midpoints of the two legs.

Connection to coordinate Connection to coordinate geometrygeometry

Trapezoid and its properties. (Coordinate GeoTrapezoid and its properties. (Coordinate Geometry)metry)

Trapezoid area and perimeter. (CoorTrapezoid area and perimeter. (Coordinate Geometry)dinate Geometry)

WebsitesWebsites

Mathopenref.comMathopenref.com Coolmath.comCoolmath.com