Properties of Quadrilaterals Any four sided polygon is a quadrilateral. We’ll study special quadrilaterals in this section: Trapezoid (U.S) or Trapezium (U.K) Parallelogram Rhombus Rectangle Square Kite

A KITE 2 pair of consecutive congruent sides Opposite sides are NOT congruent Diagonals are perpendicular Notice only ONE diagonal is bisected

Properties of a trapezoid A trapezoid has one and only one pair of parallel sides.

Properties of parallelograms Opposite sides of a parallelogram are parallel Opposite sides are congruent Opposite angles of a parallelograms are congruent. Diagonals of a parallelogram bisect each other Consecutive angles of a parallelogram are supplementary supplementary

Properties of a Rhombus (Rhombi) A rhombus is a parallelogram (this means it has ALL of the characteristics of a parallelogram) In addition: A rhombus has four congruent sides The diagonals of a rhombus are perpendicular The diagonals bisect opposite angles

Properties of Rectangles A rectangle is a parallelogram (this means it has ALL the characteristics of a parallelogram) IN ADDITION: Four right angles The diagonals of a rectangle are congruent and they bisect each other

Properties of Squares A square is a parallelogram, a rectangle, and a rhombus (It has ALL those characteristics!!!) Has four congruent sides Has four right angles The diagonals of a square: bisect each other are congruent are perpendicular. Bisect opposite angles

Practice Problems. Study Carefully and then take your test. Is this statement true or false. Explain your answer. All rhombuses are squares A rhombus has four congruent sides, but some may or may not have right angles. The statement is false.

Is this statement true or false. Explain your answer. Some trapezoids are squares A square has two sets of parallel sides, but a trapezoid has only one set of parallel sides. The statement is false.

Is this statement true or false. Explain your answer. Some parallelograms are squares. A square has all the properties of a parallelogram, so some parallelograms do have equal sides and right angles; however, some do not. The statement is true.

Is this statement true or false. Explain your answer All squares are rectangles A square has four right angles. A rectangle also has four right angles. So a square is a rectangle. The statement is true.

Is this statement true or false. Explain your answer All rectangles are squares A square has four right angles and four (2 pairs of) congruent sides. A rectangle has four right angles and 2 (a pair of) congruent sides. The statement is false.

Is this statement true or false. Explain your answer Some rectangles are squares. If the rectangle has four congruent sides, then it is a square. The statement is true.

Classwork Answer these questions. Give your reasons. (1.) A quadrilateral with four right angles and four congruent sides is called……………………. (2.) A quadrilateral with two four right angles and two congruent sides is called……………………….. (3.) A quadrilateral with exactly one pair of parallel sides is called……………….. (4.) Name any three quadrilaterals with exactly two pairs of parallel sides (5.) True or False: All quadrilaterals are parallelograms. (6.) True or False: Every parallelogram is a rectangle.