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.

Proof:  

∠ 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.

 

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