Warm Up May 8th Find the slope between (5, 8) and (3, -6). Find the distance, and midpoint between A and B where A(12, 4) B(5, 9). 3. Write the equation of a line that is perpendicular to the given equation 4x - 3y = 8, and goes through the point (3, 2).

QUIZ #6 You may use your notes but NOT your classmates!

Properties of Quadrilaterals

Quadrilateral Four sided polygon Closed, straight sides Examples: square, rectangle, diamond, etc.

Parallelogram A quadrilateral with both pairs of opposite sides parallel. We use the symbol

Diagonals of a Parallelogram If a quadrilateral is a parallelogram, then its diagonals BISECT each other. AC bisects DB AE = EC and DE = EB

The altitude (or height) of a parallelogram is the perpendicular distance from the base to the opposite side (which may have to be extended). In the figure above, the altitude, h, corresponding to the base AD is shown.

Parallelograms are the "parent" of some other quadrilaterals, which are obtained by adding restrictions: A rectangle is a parallelogram but with all four interior angles fixed at 90° A rhombus is a parallelogram but with all sides equal in length A square is a parallelogram but with all sides equal in length and all angles fixed at 90°

Rectangle All right angles (90°). Opposite sides are parallel and congruent. The diagonals bisect each other. The diagonals are congruent.

Rhombus All four sides are the same length. Also its diagonals are perpendicular. Opposite sides are parallel.

Square All right angles (90°). Opposite sides are parallel. All four sides are the same length. Diagonals are congruent. Also its diagonals are perpendicular.

Trapezoid A quadrilateral with exactly one pair of parallel sides

Isosceles Trapezoid A trapezoid with congruent legs A quadrilateral with exactly one pair of parallel sides

Homework Worksheet

Area and Perimeter of Quadrilaterals May 9th, 2013

Warm Up May 9th Which quadrilateral has diagonals that are perpendicular? Which quadrilateral has diagonals that are perpendicular, and all angles are (90°)? Which quadrilateral has only one set of parallel sides? What is the slope of the second diagonal of a rhombus, if the first diagonal has a slope of 5?

Rhombus, Rectangle, Square Rhombus-parallelogram with four congruent sides Rectangle- parallelogram with four right angles Square-parallelogram with four congruent sides and four right angles

Sometimes, Always, Never A rhombus is a rectangle A rhombus is a square A square is a rhombus A square is a rectangle A rectangle is a rhombus A rectangle is a square Sometimes Always ALWAYS

Perimeter of a Parallelogram. Perimeter = 2(w + h) w = base length of the parallelogram h = side length 5 ft

Area of a Parallelogram This can be found by multiplying a base by the corresponding altitude. A = bh

Perimeter of a Rectangle 30 Perimeter = 2(w+h) w = width of the rectangle h = height of the rectangle 15

Area of a Rectangle 30 Area = lw w  = width l  = length 15

Perimeter of a Rhombus Perimeter = 4s S = length of any one side

Area of a Rhombus Area = ba b is the length of the base a is the altitude (height)

Perimeter of a Square Perimeter = 4s s = length of one side

Area of a Square Area = s2 s = length of one side

Perimeter of a Trapezoid 9 cm Perimeter = a + b + c + d a, b, c, d = lengths of each side

Area of a Trapezoid b1, b2 = lengths of each base h = altitude (height)

Triangle and Rhombus Flap Four sided figure. All sides same length. Diagonals are perpendicular. Opposite sides parallel. P = 4s A = ba (altitude) Three sided figure.

Parallelogram & Rectangle Flap All right angles (90°). Opposite sides are parallel and congruent. Diagonals bisect each other. Diagonals are congruent. P = 2(w+h) A = lw Both pairs of opposite sides parallel. Diagonals BISECT each other. P = 2(w + h) A = bh

Trapezoid Flap Exactly one pair of parallel sides P = add all sides Isosceles trapezoids have congruent legs P = add all sides

Homework Worksheet