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

Section 6-6a Trapezoids

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

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

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

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

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

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

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

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

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

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

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

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

The length of the base of a trapezoid is 65, the midsegment is 51, and the other base is 3x + 7. What is the value of x? Example 3

The length of the base of a trapezoid is 12, the midsegment is 36, and the other base is 6x + 18. What is the value of x? Example 3

Section 6-6a Worksheet Homework