1. Lesson:
6.6 Trapezoids
Objectives:
To Identify the PROPERTIES of TRAPEZOIDS
To Recognize and Apply the PROPERTIES of a
TRAPEZOIDS to SOLVE Problems
To DEFINE a MEDIAN for a TRAPEZOID and
CALCULATE its LENGTH
To Identify SPECIAL PROPERTIES of
ISOSCELES Trapezoids

2. GEOMETRY 6.6
GEOMETRY 6.6
DEFINITION --
A TRAPEZOID is a Quadrilateral
with EXACTLY One Pair of PARALLEL Sides.

3. GEOMETRY 6.6
GEOMETRY 6.6
DEFINITION --
A TRAPEZOID is a Quadrilateral
with EXACTLY One Pair of PARALLEL Sides.

4. GEOMETRY 6.6
GEOMETRY 6.6
DEFINITION --
A TRAPEZOID is a Quadrilateral
with EXACTLY One Pair of PARALLEL Sides.

5. GEOMETRY 6.6
BASE -- the TWO Parallel Sides
LEGS -- the TWO Nonparallel Sides
Base
Leg
Leg
Base

6. GEOMETRY 6.6
DEFINITION:
An ISOSCELES TRAPEZOID is a Trapezoid
with CONGRUENT LEGS.
Base
Leg
Leg
Base

7. GEOMETRY 6.6
Isosceles Trapezoid Base Angles THEOREM
The BASE Angles of an isosceles Trapezoid
are

8. GEOMETRY 6.6
Trapezoid -- Isosceles Sides Theorem
If the BASE angles of a trapezoid are CONGRUENT,
then the Trapezoid is

9. GEOMETRY 6.6 A B ? 87 ? ? D C

10. GEOMETRY 6.6 A B ?
5x + 3 ?
10x - 3 D C

11. GEOMETRY 6.6 A B
6x + 7
9x - 5 D C

12. GEOMETRY 6.6
Do the DIAGONALS of a Trapezoid
BISECT each other?

13. GEOMETRY 6.6
Are the DIAGONALS of a Trapezoid
CONGRUENT?

14. GEOMETRY 6.6
THEOREM
The DIAGONALS of an ISOSCELES Trapezoid
are CONGRUENT.

15. GEOMETRY 6.6
DEFINITION -- MEDIAN of a Trapezoid
The MEDIAN of a Trapezoid is the
SEGMENT that Joins the MIDPOINT of the LEGS.

16. A B
GEOMETRY 6.6
GEOMETRY 6.6 X Y
THEOREM –
The MEDIAN of a Trapezoid is
PARALLEL to its bases. C D

17. A B
GEOMETRY 6.6 X Y
THEOREM –
The MEDIAN of a Trapezoid is
PARALLEL to its bases.
HALF the SUM of the LENGTHS of the Two Bases. C D

18. GEOMETRY 6.6 A 20 B
What is CD? 15 X Y C D

19. GEOMETRY 6.6 A B
What is AB? 19 X Y C D 13

20. GEOMETRY 6.6 A 28 B
What is the LENGTH
of the MEDIAN? X Y C 14 D

21. GEOMETRY 6.6 A
5X - 5 B
Find XY.
3X + 6 X Y
4X - 4 C D

22. GEOMETRY 6.6 A
3X + 4 B
Find CD.
2X + 6 X Y
4X - 13 C D

23. GEOMETRY 6.6
ABCD is an Isosceles Trapezoid. A B
TRUE or FALSE? E
AC = BD D C

24. U
GEOMETRY 6.6 E Q
QU = x2
AD = 16
Find x D F A
QUAD is an Isosceles Trapezoid

25. U
GEOMETRY 6.6 E Q
QE = 17
Find AF D F A
QUAD is an Isosceles Trapezoid

26. U
GEOMETRY 6.6 E Q D F A
QUAD is an Isosceles Trapezoid

27. GEOMETRY 6.6
ABCD is an Isosceles Trapezoid. A B
Given: E 1 2
Prove: D C

28. B. ABCD is a quadrilateral with vertices A(5, 1), B(–3, 1), C(–2, 3), and D(2, 4). Determine whether ABCD is an isosceles trapezoid. Explain.

29. GEOMETRY 6.6
You should be able to:
Name PROPERTIES to Identify a TRAPEZOID
Name SPECIAL PROPERTIES of an ISOSCELES
TRAPEZOID
CALCULATE Values of Bases and MEDIANS of
TRAPEZOIDS

30. GEOMETRY 6.6