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.