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Warm up. x = -7, -2. x = -5, 3. x = 10, -3. Factor & Solve: x 2 + 9x + 14 = 0 x 2 + 2x -15 = 0 x 2 – 7x + 15 =45. 2. √4 = _____ (this has 2 answers) √9 = _____ (this has 2 answers) √3 + √3 = _____ Use substitution to solve: y = 3x + 4 and 3x + 2y = 17. 2 and -2.

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warm up

Warm up

x = -7, -2

x = -5, 3

x = 10, -3

Factor & Solve:

x2 + 9x + 14 = 0

x2 + 2x -15 = 0

x2 – 7x + 15 =45

  • 2. √4 = _____ (this has 2 answers)
  • √9 = _____ (this has 2 answers)
  • √3 + √3 = _____
  • Use substitution to solve:
  • y = 3x + 4 and 3x + 2y = 17

2 and -2

3 and -3

2 √ 3

X = 1, y = 7

3 2 properties of quadrilaterals

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
Properties of a TRAPEZIUM:A quadrilateral with NO parallel sides.
  • 2 pair of consecutive congruent sides
  • Opposite sides are NOT congruent
  • Diagonals are perpendicular
    • Notice only ONE diagonal

is bisected

A special Trapezium is a KITE

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

supplementary

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
properties of a rhombus rhombi
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
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
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
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