#### Transcript 3.2 Properties of Quadrilaterals

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.