Axioms & Theorems

Class IX

Theorem 5.1: Two distinct lines cannot have more than one point in common. 

Axiom 6.1: If a ray stands on a line, then the sum of two adjacent angles so formed is 180°. 

Axiom 6.2: If the sum of two adjacent angles is 180°, then the non-common arms of the angles form a line. 

Axiom 6.3: If a transversal intersects two parallel lines, then each pair of corresponding angles is equal. 

Axiom 6.4: If a transversal intersects two lines such that a pair of corresponding angles is equal, then the two lines are parallel to each other. 

Axiom 7.1 (SAS congruence rule): Two triangles are congruent if two sides and the included angle of one triangle are equal to the two sides and the included angle of the other triangle. 

Theorem 7.1 (ASA congruence rule): Two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of other triangle. 

Class X

Theorem 1.1 (Euclid’s Division Lemma): Given positive integers a and b, there exist unique integers q and r satisfying a = bq + r, 0 ≤ r < b. 

Theorem 1.2 (Fundamental Theorem of Arithmetic): Every composite number can be expressed ( factorised) as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur.