What are Axioms and theorems?
Answers
Axioms the truth or general fact that can be taken as granted, they can't be proved. In fact, they can be used to prove other theorems.
Theorems are the rule or the principle that can be proved or can be shown to true.
Answer:
Axiom 1
If a ray stands on a line, then the sum of two adjacent angles so formed is 180°.
Axiom 2
If the sum of two adjacent angles is 180°, then the non-common arms of the angles form a linear pair.
Axiom 3
Corresponding Angle Axiom: If a transversal intersects two parallel lines, then each pair of corresponding angles are equal.
Theorem 1
Vertically opposite angles are congruent.
Theorem 2
If a transversal intersects two parallel lines then each pair of alternate interior angles are equal.
Theorem 3
If a transversal intersects two parallel lines such that a pair of alternate interior angles is equal then the two lines are parallel.
Theorem 4
If a transversal intersects two parallel lines then each pair of co interior angles are supplementary.
Theorem 5
If a transversal intersects two parallel lines such that a pair of co interior angles are supplementary then the two lines are parallel.
Theorem 6
Lines which are parallel to the same line are parallel to each other.
Theorem 7
The sum of the angles of a triangle is 180°.