1. 6.6 Trapezoids and Midsegment Theorem

2. Warm up 3 3 2 2

3. Objective:
Use properties of trapezoids.

4. Trapezoid The parallel sides are called the bases.
A trapezoid is a quadrilateral with one pair of parallel sides.
The parallel sides are called the bases.
The non-parallel sides are called the legs.

5. Properties of Isosceles Trapezoids
If a trapezoid is isosceles, then each pair of base angles is congruent.

6. Properties of Isosceles Trapezoids
If a trapezoid has a pair of congruent base angles, then it is isosceles.

7. 1) PQRS is an isosceles trapezoid. Find the missing angle measures.
180-50=130 50

8. 2) ABCD is an isosceles trapezoid. Find the missing angle measures.
180-75=105 75

9. 2) ABCD is an isosceles trapezoid. Find the missing angle measures.
100
180-80=105

10. Midsegment of a trapezoid:
The midsegment of a trapezoid is the segment that connects the midpoints of its legs.
Midsegment

11. PROPERTY OF A MIDSEGMENT of a TRAPEZOID
The length of the midsegment is half of the sum of the length of the bases
**taking the average**
Top + Bottom
= midsegment 2

12. Find the length of the midsegment DG of trapezoid CEFH. c)
Top + Bottom
= midsegment 2

13. d) Find the length of the midsegment MN of the trapezoid.
Top + Bottom
= midsegment 2

14. e) Find the length of the midsegment MN of the trapezoid.
Top + Bottom
= midsegment 2

15. f) Find the length of the midsegment MN of the trapezoid.
Top + Bottom
= midsegment 2

16. Example 3: Solve for x. g) 2 2

17. Example 3: Solve for x. h) 2 2

18. Example 3: Solve for x. i) 2 2

19. Example 3: Solve for x. j) 2 2

20. Example 3: Solve for x. k) 2 2