5.11 Use Properties of Trapezoids and Kites. Vocabulary  Trapezoid – a quadrilateral with exactly one pair of parallel sides. Base Base Angle Leg.

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Presentation transcript:

5.11 Use Properties of Trapezoids and Kites

Vocabulary  Trapezoid – a quadrilateral with exactly one pair of parallel sides. Base Base Angle Leg

 If the legs of the trapezoid are congruent, then the trapezoid is an isosceles trapezoid.  The midsegment of a trapezoid is the segment that connects the midpoints of its legs.

 A kite is a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent.

Theorems about isosceles trapezoids...  If a trapezoid is isosceles, then each pair of base angles is congruent.  If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid.  A trapezoid is isosceles if and only if its diagonals are congruent.

Midsegment Theorem for Trapezoids:  The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases.  ½ (b 1 +b 2 ) = length of midsegment

Properties of Kites:  If a quadrilateral is a kite, then its diagonals are perpendicular.  If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.