PptxGenJS Presentation

[Audio] LETS DISCUSS ABOUT ILLUSTRATE THE NEED FOR AN AXIOMATIC STRUCTURE OF A MATHEMATICAL SYSTEM IN GENERAL AND IN GEOMETRY.

[Audio] HELLOILLUSTRATE THE NEED FOR AN AXIOMATIC STRUCTURE OF A MATHEMATICAL SYSTEM IN GENERAL AND IN GEOMETRY.

[Audio] Perpendicular lines - the lines that intersect at a point forming a right angle. Line - undefined term is a one-dimensional figure that has infinite points and extends indefinitely in opposite direction. Transitive property - is axiom of equality is represented by the illustration below..

[Audio] Perpendicular bisector - A line which passes through the midpoint of segment at right angles.

[Audio] Angle – A figure is formed when two noncollinear rays meet in a common point. Linear pair theorem – A triangular kite IMC has the following interior angles, 50, 50°, and 80°. Liza concluded that the kite is an Isosceles triangle. This theorem would support her conclusion.

S. Symmetric property is an axiom of equality, which is what the illustrations below represent..

[Audio] Point – is undefined term is represented by a dot Line -undefined term is represented by the edge of a ruler. Symmetric property is an axiom of equality, which is what the illustrations below represent Reflexive property - axioms of equality state that for all real numbers p and q, if p = q, then q = p..

[Audio] Plane - undefined term has a specific position but has no dimension or direction Top of the table - represents a plane Supplementary angles - Two angles with sum equal to 180° An axiomatic system is a set of Undefined and defined terms, Guesses, Doubts, And Axioms. Consistency is a necessary requirement for an axiomatic system to be logically valid.

[Audio] Diagonal - A line which passes through the midpoint of segment at right angles Points A, B, C are collinear and B is between A and B, then AB = AC = BC represents the Segment Addition Postulate Congruent angle has the same measure A Scalene triangle is a type of triangle in which all three sides have different lengths. So, with two sticks of the same length and one shorter stick, you can create a scalene triangle without cutting the sticks..

[Audio] EXAMPLE The tip of a pen does not represent a plane. A consistent axiomatic system does NOT contradict do what to itself. Intersecting lines - forming four right angles best describe a perpendicular line. Congruent segments – A line perpendicular to a given segment, which divides it into two equal line segments..

[Audio] A condition exists if an axiomatic system is independent based on the other axioms. Isometry - An illustration define the undefined terms so that the axioms are true. A Mathematical set is a list of undefined terms together with a list of axioms (presupposed to be "true"), a definition for proving theorems, and other components of a mathematical system..

[Audio] ALWAYS REMEMBER Only one models can be used to illustrate axiomatic systems. Axiom - presupposed to be "true" Independent - cannot be proven from other presupposed axioms..

[Audio] I hope you found this lesson informative. Thank you.