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2. Geometry Section 6.6 Outcomes: - You will identify special quadrilaterals by their properties. - You will prove that a quadrilateral is a special type of quadrilateral.

3. Section 6.6 – Special Quadrilaterals The types of quadrilaterals can be placed in a “family tree” like below: Each shape has the qualities of the shape above it. For instance, since a parallelogram has opposite angles congruent, so does a rhombus, a rectangle, and a square. PARALLELOGRAM RECTANGLE SQUARE

4. YES NO

5. EXAMPLE 2. ABCD has at least two congruent consecutive sides. What quadrilaterals meet this condition? Rhombus Square Kite

6. Example 3. The diagonals of RSTQ are perpendicular. What quadrilaterals meet this condition? Rhombus Square Kite

7. Example 4. Put an X in the box if the shape always has the given property. PropertyParallelogramRectangleRhombus Square Trapezoid Kite Both pairs of opposite sides are congruent. Diagonals are congruent. (X only if Isosceles Trap) Diagonals are perpendicular. Diagonals bisect one another. Consecutive angles are supplementary. Exactly one pair of opposite angles is congruent. Exactly one pair of opposite sides is parallel. XXXX XX X X X X X X X X X X X X X

8. Example 5. Decide whether the following statements are always, sometimes, or never true. (a) Diagonals of a trapezoid are congruent. (b) Opposite sides of a rectangle are congruent. (c) A square is a rectangle. (d) All angles of a parallelogram are congruent. (e) Opposite angles of an isosceles trapezoid are congruent. (f) The diagonals of a parallelogram are perpendicular. Sometimes Always Sometimes Never Sometimes