## Two distinct lines cannot have more than one point in common.

__
Given
__
: Two distinct lines l
_{
1
}
and l
_{
2
}

__
To Prove
__
: l
_{
1
}
and l
_{
2
}
cannot have more than 1 point in common

__
Proof
__
: We will prove this by contradiction.

Let l
_{
1
}
& l
_{
2
}
have two points in common, P & Q.

Now, by
Axiom 5.1

Given two distinct points, there is a unique line that passes through them.

Thus, only one line passes through two distinct points P & Q.

But here we assumed both l
_{
1
}
& l
_{
2
}
pass through P & Q.

So, our assumption is wrong.

Therefore,

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

Hence proved

Thus, only one line passes through two distinct points P & Q.

But here we assumed both l
_{
1
}
& l
_{
2
}
pass through P & Q.

So, our assumption is wrong.

Therefore,

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

Hence proved