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Trapezoids and
Kites
Section 7.5
Trapezoid Definition
• A trapezoid is a quadrilateral with exactly one pair
of parallel sides. These sides are the bases.
Definition of
Isosceles Trapezoid
• If the legs of a trapezoid are congruent, then the
trapezoid is an isosceles trapezoid.
Theorem
• If a trapezoid is isosceles, then each pair of base
angles is congruent.
Theorem
• If a trapezoid has a pair of congruent base angles,
then it is an isosceles trapezoid.
Theorem
• A trapezoid is isosceles if and only if its diagonals are
congruent.
Midsegment Definition
• The midsegment connects the midpoints of the
legs.
Midsegment Theorem
• The midsegment of a trapezoid is parallel to each
base and its length is one half the sum of the bases.
Example:
What is the length of MN
in the diagram?
Kite Definition
• A kite is a quadrilateral that has two pairs of
consecutive congruent sides, but opposite sides are
not congruent.
Theorem
• If a quadrilateral is a kite, then its diagonals are
perpendicular.
Theorem
• If a quadrilateral is a kite, then exactly one pair of
opposite angles are congruent.
Example:
What is the measure of
angle D in the kite below?
p. 406
Practice
• p. 407: 7-18, 21-24