Trapezoids and Kites Section 8.5.

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Presentation transcript:

Trapezoids and Kites Section 8.5

Trapezoid Definition A trapezoid is a quadrilateral with exactly one pair of parallel sides. These sides are the bases.

Is this a trapezoid?

Isosceles Trapezoid If the legs of a trapezoid are congruent, then the trapezoid is an isosceles trapezoid.

Theorem 8.14 If a trapezoid is isosceles, then each pair of base angles is congruent.

Theorem 8.15 If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid.

Theorem 8.16 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.

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 8.18 If a quadrilateral is a kite, then its diagonals are perpendicular.

Theorem 8.19 If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.

What is the measure of angle D in the kite below?

Assignment Pg. 546 #7-27 odds