|Class 9 Maths Lines and Angles||Lines parallel to same line|
Lines parallel to same line
Theorem 6 : Lines which are parallel to the same line are parallel to each other
Since this is a theorem, let’s try to prove it.
To prove: m is parallel to p, given m is parallel to n & n is parallel to p.
∠ 1 = ∠ 2 (Corresponding angle Axiom: m is parallel to n) – (i)
∠ 2 = ∠ 3 (Corresponding angle Axiom: n is parallel to p) – (ii)
Using I & ii, we get ∠ 1 = ∠ 3, but these are corresponding angles.
This lime m is parallel to p using corresponding Angle Axiom.