1. Warm up:
Can you conclude that the parallelogram is a rhombus, a rectangle, or a square? Explain.
For what value of x is parallelogram ABCD a rectangle?
Given WRST is a parallelogram and WS is congruent to RT, how can you classify WRST? Explain.

2. 6.6/6.7 - Trapezoids and Kites AND polygons in the coordinate plane
I can verify and use properties of trapezoids and kites. I can classify polygons in the coordinate plane.

3. The nonparallel sides are called legs.
Trapezoids
A trapezoid is a quadrilateral with exactly one pair of parallel sides. The parallel sides of a trapezoid are called bases.
The nonparallel sides are called legs.
The two angles that share a base of a trapezoid are called base angles. A trapezoid has two pairs of base angles.

4. An isosceles trapezoid is a trapezoid with legs that are congruent.
ABCD below is an isosceles trapezoid. The angles of an isosceles trapezoid have some unique properties.

5. Theorem 6 – 19 Theorem 6 – 19 Theorem If… Then…
If a quadrilateral is an isosceles trapezoid, then each pair of base angles is congruent.

6. Problem: Finding Angle Measures in Trapezoids
CDEF is an isosceles trapezoid and m<C = 65. What are m<D, m<E, and m<F?

7. Problem: Finding Angle Measures in Trapezoids
In the diagram, PQRS is an isosceles trapezoid and
m<R = What are m<P, m<Q, and m<S?

8. Problem: Finding Angle Measures in Trapezoids
RSTU is an isosceles trapezoid and m<S = 75. What are m<R, m<T, and m<U?

9. Theorem 6 – 20 Theorem 6 – 20 Theorem If… Then…
If a quadrilateral is an isosceles trapezoid, then its diagonals are congruent.

10. Trapezoid Midsegment Theorem
In Chapter 5 – 1, we learned about midsegments of triangles. Trapezoids also have midsegments. The midsegment of a trapezoid is the segment that joins the midpoints of its legs. The midsegment has two unique properties.
Trapezoid Midsegment Theorem
Theorem
If…
Then…
If a quadrilateral is a trapezoid, then
The midsegment is parallel to the bases, and
The length of the midsegment is half the sum of the lengths of the bases.

11. Problem: Using the Midsegments of a Trapezoid
QR is the midsegment of trapezoid LMNP. What is x?

12. Problem: Using the Midsegments of a Trapezoid
MN is the midsegment of trapezoid PQRS. What is x? What is MN?

13. Problem: Using the Midsegments of a Trapezoid
TU is the midsegment of trapezoid WXYZ. What is x?

14. The angles, sides, and diagonals of a kite have certain properties.
A kite is a quadrilateral with two pairs of consecutive sides congruent and no opposite sides congruent.
The angles, sides, and diagonals of a kite have certain properties.
Theorem 6 – 22
Theorem
If…
Then…
If a quadrilateral is a kite, then its diagonals are perpendicular.

15. Problem: Finding Angle Measures in Kites
Quadrilateral DEFG is a kite. What are m<1, m<2, and m<3?

16. Problem: Finding Angle Measures in Kites
Quadrilateral KLMN is a kite. What are m<1, m<2, and m<3?

17. Problem: Finding Angle Measures in Kites
Quadrilateral ABCD is a kite. What are m<1 and m<2?

18. Concept Summary: Relationships Among Quadrilaterals

19. After: Lesson Check What are the measures of the numbered angles?
What is the length of the midsegment of a trapezoid with bases of length 14 and 26?

20. After: Lesson Check Is a kite a parallelogram? Explain.
How is a kite similar to a rhombus? How is it different? Explain.
Since a parallelogram has two pairs of parallel sides, it certainly has one pair of parallel sides. Therefore, a parallelogram must also be a trapezoid. What is the error in this reasoning? Explain.

21. Homework:
Page 394, #8-34 even
AND
Page 403, #5-7 all, 10