1. created by chris markstrum © 2005 State Standards for Geometry 4: Prove basic theorems involving congruence & similarity. 7: Prove & use theorems involving parallel lines and properties of quadrilaterals. 12: Find & use side and angle measures of triangles and polygons 6.5 Trapezoids and Kites

2. created by chris markstrum 2005 definition Trapezoid A quadrilateral with exactly one pair of parallel sides Bases:the parallel sides Legs:the non-parallel sides Isosceles:when the legs are congruent base 1 base 2 leg AB CD

3. created by chris markstrum 2005 definition base 1 base 2 leg W X Y Z Trapezoid A quadrilateral with exactly one pair of parallel sides Bases:the parallel sides Legs:the non-parallel sides

4. created by chris markstrum 2005 definition Kite A quadrilateral with two pairs of congruent consecutive sides. F G H E

5. created by chris markstrum 2005 definition P Q R S Kite A quadrilateral with two pairs of congruent consecutive sides.

6. created by chris markstrum 2005 theorem If a trapezoid is isosceles, then each pair of base angles is congruent. AB CD

7. created by chris markstrum 2005 theorem If a trapezoid has a pair of congruent base angles then it is an isosceles trapezoid. AB CD

8. created by chris markstrum 2005 theorem A trapezoid is isosceles if and only if its diagonals are congruent. AB CD

9. created by chris markstrum 2005 theorem The midsegment of a trapezoid is parallel to each base A B CD EF and its length is the average of the lengths of the bases.

10. created by chris markstrum 2005 theorem The diagonals of a kite are perpendicular. A B C D

11. created by chris markstrum 2005 theorem The angles between the non-congruent sides of a kite are congruent. A B C D

12. created by chris markstrum 2005 Example CDEF is an isosceles trapezoid. C D EF CE = 10 95 o

13. created by chris markstrum 2005 W Example The vertices of WXYZ are W ( - 1, 2), X (3, 0), Y (4, - 3), Z ( - 4, 1) Show that WXYZ is an isosceles trapezoid. X Y Z

14. created by chris markstrum 2005 W Example X Y Z The vertices of WXYZ are W(-1, 2), X(3, 0), Y(4, -3), Z(-4, 1) Show that WXYZ is an isosceles trapezoid.

15. created by chris markstrum 2005 W Example X Y Z The vertices of WXYZ are W(-1, 2), X(3, 0), Y(4, -3), Z(-4, 1) Show that WXYZ is an isosceles trapezoid.

16. created by chris markstrum 2005 P Q R S Example PQRS is a trapezoid with the given measurements. M N 8 10 85 o 110 o

17. created by chris markstrum 2005 Example 85 o 110 o PQRS is a trapezoid with the given measurements. P Q R S M N 8 10

18. created by chris markstrum 2005 Example PQRS is a trapezoid with the given measurements. 85 o 110 o P Q R M N 8 10

19. created by chris markstrum 2005 H I J L Example HIJK is a kite. Find HP 5 P 2

20. created by chris markstrum 2005 70 o D E F G Example DEFG is a kite. 125 o x + 30 x 40 o 125 o

21. created by chris markstrum 2005 Summary What are the characteristics of a trapezoid? What are the characteristics of a kite? Compare a kite and a rhombus.