Transcript 3.2 Properties of Quadrilaterals

Warm up
1. Factor & Solve:
a. x2 + 9x + 14 = 0
x = -7, -2
b. x2 + 2x -15 = 0
x = -5, 3
c. x2 – 7x + 15 =45
x = 10, -3
2. √4 = _____
2 and -2
(this has 2 answers)
3 and -3
3. √9 = _____
(this has 2 answers)
2√3
4. √3 + √3 = _____
5. Use substitution to solve:
y = 3x + 4 and 3x + 2y = 17
X = 1, y = 7
3.2 Properties of
Quadrilaterals
♥Any four sided polygon is a quadrilateral.
♥We’ll study special quadrilaterals in this section:
♥Trapezoid
♥Trapezium
♥Parallelogram
♥Rhombus
♥Rectangle
♥Square
♥Kite
Properties of a TRAPEZIUM:
A quadrilateral with NO parallel sides.
A special Trapezium is 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
Cut and sort
• Go to the back of the room and get
worksheets 2-15A and 2-15B and a pair of
scissors
• Your instructions are on 2-15B
• Have fun Ü
• Then complete 2-16