7/1/ : Properties of Quadrilaterals Objectives: a. Define quadrilateral, parallelogram, rhombus, rectangle, square and trapezoid. b. Identify the properties of quadrilaterals and relationships between properties.

7/1/ : Properties of Quadrilaterals Quadrilateral A polygon is a quadrilateral iff it has exactly 4 sides.

7/1/ : Properties of Quadrilaterals Trapezoid A quadrilateral is a trapezoid iff it has exactly one pair of parallel sides.

7/1/ : Properties of Quadrilaterals Isosceles Trapezoid A trapezoid is isosceles iff the non parallel sides (legs) are congruent.

7/1/ : Properties of Quadrilaterals Parallelogram A quadrilateral is a parallelogram iff both pair of opposite sides are parallel.

7/1/ : Properties of Quadrilaterals Rhombus A quadrilateral is a rhombus iff it has 4 congruent sides.

7/1/ : Properties of Quadrilaterals Rectangle A quadrilateral is a rectangle iff it has 4 right angles.

7/1/ : Properties of Quadrilaterals Square A quadrilateral is a square iff it has 4 congruent angles and 4 congruent sides.

7/1/ : Properties of Quadrilaterals Kite A quadrilateral is a kite iff it has 2 distinct pairs of congruent and adjacent sides.

7/1/ : Properties of Quadrilaterals Properties of a Parallelogram Theorem If a quadrilateral is a parallelogram, then: a. Both pairs of opposite angles are congruent. b. Both pairs of opposite sides are congruent. c. Diagonals bisect each other. d. Consecutive angles are supplementary.

7/1/ : Properties of Quadrilaterals Properties of a Rhombus Theorem If a quadrilateral is a rhombus, then: a. It is a parallelogram. b. Its diagonals are perpendicular.

7/1/ : Properties of Quadrilaterals Properties of a Rectangle Theorem If a quadrilateral is a rectangle, then: a. It is a parallelogram. b. Its diagonals are congruent.

Which of the following is NOT a property of all rectangles? A) diagonals are perpendicular B) diagonals are congruent C) consecutive sides are perpendicular D) consecutive angles are congruent E) consecutive angles are supplementary 7/1/ : Properties of Quadrilaterals

Which of the following is a property of squares, but not rhombi? A) Diagonals are perpendicular B) Diagonals are congruent C) Consecutive sides are congruent D) Consecutive angles are supplementary E) Opposite angles are congruent 7/1/ : Properties of Quadrilaterals

7/1/ : Properties of Quadrilaterals Properties of a Square Theorem If a quadrilateral is a square, then: a. It is a parallelogram, a rhombus, a rectangle and a kite. b. Its diagonals are perpendicular, congruent and they bisect each other.

7/1/ : Properties of Quadrilaterals Quadrilaterals quadrilaterals trapezoids parallelograms kites

7/1/ : Properties of Quadrilaterals Parallelograms rhombi rectangles squares parallelograms

7/1/ : Properties of Quadrilaterals In parallelogram ABCD, m ∠ A= 48°. What are m ∠ B, m ∠ C and m ∠ D?

To which family of quadrilaterals does a rectangle necessarily belong? A) kites B) parallelograms C) rhombi D) squares 7/1/ : Properties of Quadrilaterals

7/1/ : Properties of Quadrilaterals Assignment pages , # 9-41 (all).