The transitive property of equality is defined as, “Let a, b and c be any three elements in set A, such that a=b and b=c, then a=c”.
In geometry, transitive property, for any three geometrical measurements, sides or angles, is defined as, “If two segments (or angles) are each congruent with a third segment (or angle), then they are congruent with each other”.
Image courtesy: cms.uhd.edu
The substitution property of equality states that “for any real numbers “a” and “b” if a = b then a can be substituted for b”. In simple words, a=b implies that b=a, therefore in any algebraic expression or equation, we can replace any ‘a’ with ‘b’ or any ‘b’ with ‘a’.
For example, if you are asked to solve an algebraic expression (x+7)/2 and it is given that x=5, then solve the expression by substituting the value of x. By putting x=5 in the above expression you get (5+7)/2 which is equal to 12/2, which equals 6. So, according to substitution property, if two values are equal to one another, they can be comfortably substituted for each other.
Besides algebra, substitution property is also used in geometry. When used in geometry, substation property of equality states that “if two geometric measurements are congruent then they can be easily replaced with one another in a statement involving one of them”.
These geometric objects can be two angles, two line segments, triangles etc. Essentially, the substitution property of equality in geometry says that if two things are equal in magnitude, it does not matter which one you use.
Image courtesy: cliffmass.blogspot.com