Math

• it is a branch of mathematics


  geometry
• What are the 4 types of mathematical system?

  Undefined terms,Defined terms,Axioms/Postulates and Theorems
• it Cannot be precisely defined,simply an idea,can only be described


  undefined terms
• what are the types of undefined terms?

  line,point and plane
• it has no length,width or thickness;occupies no space or has no dimensions

  point
• has infinite length,no width nor thickness and a straight line

  line
• a flat surface extending infinitely in all directions

  plane
• how to name a point?

  it is named using a capital letter
• how to name a line?


  named by two points

  may also be named by one small letter or a number
• how to name a plane?

  using capital letter written at the corner or using 3 non-collinear points in it
• have formal definition


  defined terms
• accepted as true without a proof


  axioms/postulates
• assumptions specific to geometry

  postulates
• generally statements used throughout mathematics

  axioms
• a statement that can be proven


  theorems
• a+b=b+a or a.b=b.a is an example of?

  commutative axioms
• a+(b+c)=(a+b)+c or a(bc)=ab(c) is an example of?

  associative axioms
• a(b+c)=(ab)+(bc) is an example of?

  distributive axioms
• a=a is an example of?


  reflexive axioms
• if a=b,then b=a is an example of?


  symmetric axioms
• if a<b,and b<c,then a<c is an example of?


  transitive axiom
• if a=b,then a+c=b+c is an example of?


  addition axiom
• if a=b,then ac=bc is an example of?

  multiplication axiom
• if a+(-a)=(-a)+a=0 is an example of?

  existence of additive inverse
• a.a‐¹=a‐¹.a=1 for a is not equal to 0 is an example of?

  existence of multiplicative inverse
• for any real number a,a+0=0+a=a is an example of?

  existence of additive identity
• for any real number a,a.1=1.a=a is an example of?

  existence of multiplicative identity
• a<b or a=b or b<a is an example of?

  trichotomy theorem
• it is the union of points and all the points between them.

  line segment
• a point in a line segment that divides it into two equal parts

  midpoint
• points that lie on the same line


  collinear points
• points that lie on the same plane


  coplanar points
• a part of a line that has one endpoint and goes infinitely in one direction


  ray
• lines in a plane that do not intersect

  parallel lines
• two lines that intersect and forms a right angle


  perpendicular lines
• the union of two non collinear with a common endpoint


  angle
• angles that measured less than 90°

  acute angles
• angles that measured more than 90° but less than 180°

  Obtuse angle
• Angles that measured more than 180° but less than 360°


  Reflex angle
• angles that has common vertex and common side

  adjacent angles