Trapezoids Jude Saint-Jean DapoBrandonPeriod:12

Definition A quadrilateral which has at least 1 pair of parallel sides A quadrilateral which has at least 1 pair of parallel sides A trapezoid with 1 pair of congruent sides A trapezoid with 1 pair of congruent sides

Properties of sides The bases (top and bottom) of an isosceles trapezoid are parallel. The bases (top and bottom) of an isosceles trapezoid are parallel. Opposite sides of an isosceles trapezoid are congruent. Opposite sides of an isosceles trapezoid are congruent. The angles on either side of the bases are congruent. The angles on either side of the bases are congruent. The bases (top and bottom) of a trapezoid are parallel. 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. That's it. No sides needs to be congruent and no angles need to be congruent.

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.

Proof Given: <a=102 & <d is adjacent to <a & it’s an isosceles trapezoid Given: <a=102 & <d is adjacent to <a & it’s an isosceles trapezoid <a = 102 <a is congruent to <b <a+<b+<c+<d = 360 <c is congruent to <d <d is supp. to <a Prove: <d is supp. to <a Prove: <d is supp. to <aGiven Same side interior angles Angle property of quadrilateral(1,2) Same side interior angles(3) Addition property(4)

Properties of diagonals The diagonals (not show here) are congruent. The diagonals (not show here) are congruent. Nothing special happens with the diagonals. Nothing special happens with the diagonals.

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

formulas Perimeter = a + b + c + B Perimeter = 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 need... So, multiply by 1/2. But, this is double of what we need... So, multiply by 1/2.

Other facts Altitude: The aaaa llll tttt iiii tttt uuuu dddd eeee of a trapezoid is the pppp eeee rrrr pppp eeee nnnn dddd iiii cccc uuuu llll aaaa rrrr 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 and its properties. (Coordinate Geometry) Trapezoid and its properties. (Coordinate Geometry) Trapezoid and its properties. (Coordinate Geometry) Trapezoid area and perimeter. (Coordinate Geometry) Trapezoid area and perimeter. (Coordinate Geometry) Trapezoid area and perimeter. (Coordinate Geometry) Trapezoid area and perimeter. (Coordinate Geometry)

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