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**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

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**A KITE 2 pair of consecutive congruent sides**

Opposite sides are NOT congruent Diagonals are perpendicular Notice only ONE diagonal is bisected

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**Properties of a trapezoid**

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

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**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

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**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

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**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

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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

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**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.

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**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.

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**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.

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**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.

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**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.

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**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.

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**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.

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