This document discusses properties of trapezoids and kites. It defines a trapezoid as a quadrilateral with one pair of parallel sides, and an isosceles trapezoid as having congruent legs. Theorems state that in an isosceles trapezoid, the base angles are congruent and the diagonals are congruent. A midsegment connects the midpoints of the legs and equals half the sum of the parallel sides. A kite has two pairs of congruent adjacent sides, with perpendicular diagonals and one pair of congruent opposite angles. The document provides homework problems related to these shapes.

1. 6.5 Trapezoids and kites
Base angles
Isosceles trapezoids
Midsegments

2. Trapezoid definition
A Trapezoid is a quadrilateral with only
one pair of parallel sides.
Base
Base
Leg
Leg
1
b
2
b
h
Amgle
Base
Amgle
Base
Amgle
Base
Amgle
Base

3. Isosceles Trapezoids
Isosceles Trapezoids have congruent legs.
Base
Base
Leg
Leg
1
b
2
b
h
Amgle
Base
Amgle
Base
Amgle
Base
Amgle
Base

4. Theorem
In a Isosceles Trapezoid each pair of
base angles are congruent.

5. Theorem
If a pair of base angles in a trapezoid are
congruent, then the trapezoid is an
isosceles trapezoid.

6. Theorem
In an Isosceles trapezoid the diagonals
are congruent.

7. Definition of a Midsegment
Midsegment connect the midpoints of the
legs.

8. Theorem
The Midsegment equal half the parallel
sides sum.

9. Solve for NO =
The Midsegment equal half the parallel
sides sum.

10. Definition of a Kite
A kite is a quadrilateral with two distinct
pairs of adjacent sides that are
congruent.

11. Theorem
Diagonals in a kite are perpendicular.
BD
AC 

12. Theorem
In a Kite, exactly one pair of opposite
angles are congruent.
D
B 



13. Homework
Page 359 – 362
# 10 – 24 even,
25 – 27 ,
28 – 38 even

14. Homework
Page 359 – 362
# 11 – 23 odd,
31, 33 , 35, 37,
39, 48 -52