how many theorems are there in chapter 6 = lines and angles (NCERT) , class 9 , chapter=lines and angles , please can anyone say all the theorems , if you dont know dont answer , no need to answer by saying idk .
Answers
Answer:
There are 8 theorems and 4 axioms
Step-by-step explanation:
Axioms
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.
Theorems
Theorem 6.1 : If two lines intersect each other, then the vertically opposite angles are equal.
Theorem 6.2 : If a transversal intersects two parallel lines, then each pair of alternate interior angles is equal.
Theorem 6.3 : If a transversal intersects two lines such that a pair of alternate
interior angles is equal, then the two lines are parallel.
In a similar way, you can obtain the following two theorems related to interior angles on the same side of the transversal.
Theorem 6.4 : If a transversal intersects two parallel lines, then each pair of interior angles on the same side of the transversal is supplementary.
Theorem 6.5 : If a transversal intersects two lines such that a pair of interior angles on the same side of the transversal is supplementary, then the two lines are parallel.
Theorem 6.6 : Lines which are parallel to the same line are parallel to each other
Answer:
the above answer is correct.