1. Are the following statements always, sometimes, or never true?
A parallelogram is a rectangle.
A square is a rhombus.
The diagonals of a rectangle are congruent.
The diagonals of a rhombus bisect opposite angles.
The diagonals of a square are perpendicular.
A rhombus is a parallelogram.
Problem of the Day

2. Section 6-6a Trapezoids

3. Then Now Objectives You used properties of special parallelograms.
Apply properties of trapezoids.

4. Common Core State Standards
Content Standards
G.GPE.4 – Use coordinates to prove simple geometric theorems algebraically.
G.MG.3 – Apply geometric methods to solve problems.
Mathematical Practices
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Common Core State Standards

5. Trapezoid: A quadrilateral with exactly one pair of parallel sides
Trapezoid: A quadrilateral with exactly one pair of parallel sides. Bases: The parallel sides. Legs: The nonparallel sides. Base Angles: The angles formed by the base and one of the legs.
Vocabulary

6. Isosceles Trapezoid: A trapezoid in which the legs are congruent.
Vocabulary

7. A trapezoid is isosceles if and only if its diagonals are congruent.
If a trapezoid is isosceles, then each pair of base angles is congruent.
If a trapezoid has one pair of congruent base angles, then it is an isosceles trapezoid.
A trapezoid is isosceles if and only if its diagonals are congruent.
Isosceles Trapezoids

8. To save space at a square table, cafeteria trays often incorporate trapezoids into their design. If WXYZ is an isosceles trapezoid and m∠YZW = 45, WV = 15 cm, and VY = 10 cm, find each measure.
m∠XWZ
m∠WXY XZ XV
Example 1

9. The basket shown is an isosceles trapezoid. If m∠JML = 130, KN = 6
The basket shown is an isosceles trapezoid. If m∠JML = 130, KN = 6.7 feet, and MN = 3.6 feet, find each measure. 1) m∠MJK 2) JL
Example 1

10. ABCD is an isosceles trapezoid with A(-4, -1), B(-2, 3) and C(3, 3)
ABCD is an isosceles trapezoid with A(-4, -1), B(-2, 3) and C(3, 3). Find the coordinates of D.
Example 2

11. ABCD is an isosceles trapezoid with A(5, -4), B(3, 0) and C(-4, 0)
ABCD is an isosceles trapezoid with A(5, -4), B(3, 0) and C(-4, 0). Find the coordinates of D.
Example 2

12. ABCD is an isosceles trapezoid with A(-4, 1), B(-2, 5) and C(1, 5)
ABCD is an isosceles trapezoid with A(-4, 1), B(-2, 5) and C(1, 5). Find the coordinates of D.
Example 2

13. Midsegment of a Trapezoid: The segment that connects the midpoints of the legs of the trapezoid.
Vocabulary

15. The length of the bases of a trapezoid are 10 and 20, the midsegment is 2x What is the value of x?
Example 3

16. The length of the base of a trapezoid is 65, the midsegment is 51, and the other base is 3x What is the value of x?
Example 3

17. The length of the base of a trapezoid is 12, the midsegment is 36, and the other base is 6x What is the value of x?
Example 3

18. Section 6-6a Worksheet
Homework