Trapezoids and Kites Section 7.5.

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1 Trapezoids and Kites Section 7.5

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

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

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

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

6 Theorem A trapezoid is isosceles if and only if its diagonals are congruent.

7 Midsegment Definition
The midsegment connects the midpoints of the legs.

8 Midsegment Theorem The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the bases.

9 Example: What is the length of MN in the diagram?

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

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

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

13 Example: What is the measure of angle D in the kite below?

14 p. 406

15 Practice p. 407: 7-18, 21-24