• Difference of two squares
  • a²- b² = (a + b)(a - b)
    •  x²-25= (x+5) (x-5)
    • x²-
• Trinomial perfect squares
  • a² + 2ab + b² = (a + b)(a + b) or (a + b)²
    • 3 examples
  • ^{a2 - 2ab + b2 = (a - b)(a - b) or (a - b)2}
    • 3 examples
• Difference of two cubes
  • a³ - b³
    • 3 - cube root 'em
    • 2 - square 'em
    • 1 - multiply and change
      • 3 examples
• Sum of two cubes
  • a³ + b³ 
    • 3 - cube root 'em
    • 2 - square 'em
    • 1 - multiply and change
      • 3 examples
• Binomial expansion
  • (a + b)³ = Use the pattern
  • (a + b)⁴ = Use the pattern

Zero Discriminant

• Zero Discriminant
• 1 real solution

Positive Discriminant

• Positive Discriminant, crosses the X- axis
• 2 real solutions

Negitive Discriminant

•  Positive Discriminant
• 2 real solutions

Quadrilaterals

Quadrilaterals

• four sides
• sum of the interior angles is 360 degrees

Kite

• 2 pair of congruent sides
• consective sides are not congruent

Parallelogram

• both pairs of oppisite sides are congruent
• both pairs of oppisite angles are congruent

Rectangles

• 4 right angles
• diagonals are congruent

Rhombus

• parellelogram with 4 congruent sides
• diagonals are perpendicular
• pair of oppisite angles

Square

• all sides are congruent
• angles are are congruent
•  diagonals intersect at 90 degrees

Trapizoid

• 1 pair of parellel sides

Points of Concurrency

Obtuse Triangle

Obtuse Triangle- One side is above 90 degreese.

Scalene Obtuse

Scalene obtuse- all angles are different and one angle is above 90 degreese.

Scalene acute

Scalene acute- all angles are different and 1 angle is above 90 degreese.

Isosceles obtuse

Two sides are congruent and one side is greater then 90 degrees.

Isosceles Acute

Two sides are congruent and one side is less then 90 degrees.

Acute Triangle

All three angles are different and all angles are less than 90.

Isosceles Right Triangle

An isosceles right triangle has angles of 45 degrees, 45 degrees, and 90 degrees.

Isosceles triangle

A triangle with  two equal sides, and one side is greater than 90.

AAS

  
* Anlges BC and ED are congruent
* Angles AB and FE are congruent
* Angles AC and FD are congruent

SSS

* Angles AB and YX are congruent
* Angles BC  and YZ are congruent
* Angles CA and ZX are congruent

SAS

.

• Angles D and C are congruent 
• Sides DE and  BC are congruent
• Angles E and  B are congruent

ASA

These triangles are angle side angle.

Constructing a perpendicular at a point on a line

Side Angle Side

Equilangular Triangle

 All angles and all sides are equal

Different triangles

Isosceles obtuse -Has a right angle 90 and  two equal angles
Isoscels acute -  Has a right angle less than 90
Scalene obtuse - One side is greater than 90

Scalene acute- All sides are less than 90
Scalene right - A triangle that has a right angle

Triangle classification

Angles and Sides



            Sides

• 
  
  Scalene
• 
  
  Equilateral
• 
  
  Isosceles

Angles

• Right
• Obtuse
• Acute
• Equilangular

Side Angle Side

Triangles ABCFED

Side Angle Side (SAS)

This two triangles are congruent by side angle side. Angles ABC are congruent to angles A' B' and C'.

1. Angle one is equal to angle 2      2. The lines are parrellel     3. Angles 1 and 2 are set equal to 90    4. The lines are supplementary

2 right angles

1. Add (2x-11) and 51 together and set them equal to 90

2. Subtract 11 from 51 and you get 40

3. Subtract 40 from 90 and you get 50, then divide 50 by 2

4.  x=25

5. Plug in 25

6. Add 39 and 51 and you get 90

Powerpoint on logic statements

1. Distance Formula for the points (-4,3) (6,-2)
2. Subsitute the points in the formula
(if any numbers are negitive remember to keep up with the signs)
3.Add or subtract
4. Square the numbers. this will always be a positive number.
5. Add your squares,
6. Aproximate using calculator
7.Simplify five on the square root of twentyfive.

Complementary and Suplementary angles

DFE and BAC are both acute angles, they are less than 90 degrees. They are also Complementary. DEF is a obtuse angle, more than 90 degrees. It is also Suplementary

Complemenary angles

Equals 90 degrees so it is a Complemenary angles. ABD and DCE are both Complemenary angles.

Suplementary angles

Equal 120 degrees, so they are Suplementary angles. Lines ABC and BCD are Suplementary angles.

Complementery Angle

Equals 90 degrees, angle is a Right angle. The angles ABC and CBD are complementary.

Shoes

Shoes are what i am interested in. I love shoes ! I have about 45 pair and only were about 14.