Quadrialteral Properties

Quadrilateral "Family Tree" -

Quadrilateral - 4 sided polygon

A. Kite -
1. has consecutive sides congruent but opposite sides are not.
2. the diagonals are perpendicular
3. has exactly one pair of opposite angles congruent.

B. Trapezoid -
1. Has exactly one pair of opposite sides parallel

C. Isosceles Trapezoid -
1. Has exactly one pair of opposite sides parallel
2. the non-parallel sides are congruent (legs congruent)
3. the diagonals are congruent
4. the base angles are congruent

D. Parallelogram -
1. Definition: has both pairs of opposite sides parallel
2. has both pairs of opposite sides congruent
3. has one pair of opposite sides parallel and congruent
4. has both pairs of opposite angles congruent
5. has consecutive angles supplementary
6. the diagonals bisect each other
7. the diagonals divide the parallelogram into 2 congruent triangles

E. Rhombus -
1. All of the properties of a parallelogram
2. All sides are congruent (equilateral)
3. diagonals are perpendicular
4. diagonals bisect opposite angles

F. Rectangle -
1. All of the properties of a parallelogram
2. all angles are congruent (equiangular)
3. diagonals are congruent

G. Square -
1. All the properties of a parallelogram, rhombus and rectangle

check out this website:
http://regentsprep.org/Regents/math/quad/LQuad.htm

Coordinate Geometry

Geometry - Coordinate Geometry:

check out this website:
http://regentsprep.org/Regents/mathb/1D/Coordinatelesson.htm

B(x₁, y₁) and A (x₂, y₂) is from the
Pythagorean Theorem which is:

c² = a² + b²

since a = (x₂ – x₁) and b = (y₂ – y₁)

we get

c² = (x₂ – x₁)² + (y₂ – y₁)²
so taking the square root of both sides we have our distance formula.

Here are the Slope Formula and the Midpoint Formula:

Using the following chart, if we have to prove congruent segments, we have to show they have equal length by using the distance formula.

Here is a web-site to hopefully help:

http://library.thinkquest.org/20991/geo/coordgeo.html