 Hello and welcome to the session. In this session we discussed the following question which says prove that two lines which are parallel to same line are parallel to each other that is if m parallel to l, n parallel to l then n parallel to n. Before moving on to the solution let's recall Euclid's fifth postulate. According to this we have two distinct intersecting lines cannot be parallel to the same line. This is the key idea for this question. Let's proceed with the solution now. We are given three lines m, m and n in a plane such that we have m is parallel to l, m is parallel to l that is two distinct lines m and n are parallel to the same line l and we need to prove that m is parallel to n. For this first we assume let the line m be not parallel to the line n then this means that lines m and n intersect at a unique point point p thus to the point p outside the line l there are two distinct intersecting lines cannot be parallel to the same line so since here we have that m and n are two distinct intersecting lines and this shows that m and n are both parallel to the line l so this contradicts Euclid's postulate our assumption is wrong hence we have that n is parallel to n since we had assumed let m be not parallel to n and we have got that our assumption is wrong so we say that n is parallel to n so we have proved that m is parallel to n that is we have proved that two lines which are parallel to same line are parallel to each other that is we have that if given line m parallel to line l line n parallel to line l thus implies that line m would be parallel to line n with this we complete the session hope you have understood the solution for this question.