Positive Discriminant

• Positive Discriminant
• 2 real solutions

Negative discriminant

                 Negative discriminant

                 No real solutions



Zero discriminant

• 0 discriminant
•  1 real solutions

Quadrilaterals

• 2 pair of congruent sides
• 2 pair of congruent angles
•  diagnols bisects, are congruent and perpendicular

•  a parallelogram with four congruent sides
• 2 pair of congruent angles
• diagonals bisects each other and are congruent

• 2 pair of congruent sides
• opposite angles are congruent other is non-congruent
• diagnols bisects a pair of opposite angles

• 2 pairs of congruent sides but one pair is parallel
• consecutive angles are supplementary
• bisects an angle or each other

•    one pair of  non-parallel sides called legs, if legs are congruent its a isosceles trapezoid, and one pair of parallel sides
• diagnols are congruent

• 2 pair of congruent sides and opposite sides are not congruent.
• one pair of opposite anggles are congruent other is not
• diagonals bisects angles and is perpendicular

• one pair of parallel sides one pair not
• no special angle properties or diagnol properties

Points of Concurrency

Classification of Triangles

Equilateral Triangle-An equilateral triangle is a triangle with all three sides  of equal length.

Equilangler triangle- All angles are the same.




Equilateral Triangle

 



Isosceles Triangle-An isosceles triangle is a triangle with at least two equal sides.



Isosceles Right triangle- one angle is 90 degrees and the other two angles are 45 and 45 degrees.

 




 

Isosceles Acute triangle- all angles are less than 90 degrees.

Isosceles Obtuse triangle - one angle is more than 90 degrees and two angles are less than 90 degrees.

Scalene Triangle-A triangle with all sides of different lengths.
No sides are equal and no angles are equal.


Scalene right triangle- one angle is 90 degrees and the other two are less than 90 degrees.

 



Scalene Acute triangle- All angles are less than 90 degrees.

Scalene Obtuse triangle- one angle is more than 90 degrees and the others are less than 90 degrees.

ASA,AAS,SSS,SAS

This is ASA because of the following:

• 
  
  Angles FDE and ACB are congruent angles.
• 
  
  Lines ED and BC are congruent sides
• 
  
  Angles ABC and FED are congruent angles

This is AAS because of the following:

• 
  
  Angles ACB and FDE are congruent angles.
• 
  
  Angles ABC and FED are congruent angles also.
• 
  
  Lines AB and FE are congruent sides.  

This is SSS because of the following:

• 
  
  Lines AB and FE are congruent sides.
• 
  
  Lines BC and ED are congruent sides.
• 
  
  Lines CA and DF are congruent sides also.

This is SAS because of the following:

• 
  
  Lines AB and FE are congruent sides.
• 
  
  Angles ABC and FED are congruent angles.
• 
  
  Lines BC and ED are congruent sides.

Orthocenter video

This video is about the orthocenter is the point where the three altitudes of a triangle intersect one of a triangle's points of concurrency.