Question

Prove that two distinct lines cannot have more than one point in common.

Answer 1

To prove = Lines l1 and l2 have only one point in common.
Proof =
suppose lines l1 and l2 intersect at two disticnt points say P and Q.Then l1 contains points P and Q.
Also, l2 contains points P and Q.
So two line sl1 and l2 pass through two distinct points P and Q.
But only one line can pass through two different points.   (axiom 3)
so the assumption we started with that two lines can pass through two disticnt point is wrong.
Hence, two lines cannot have more than one point in common.

:) 

Answer 2

Answer:

given: let two lines l and m

to prove: l and m have only one common point.

Proof

if possible suppose l and m have two distinct common points p and q.

Hence, p and Q lies on both the lines l and m.

Hence, line l passes through p and Q and line m also passes through p and q.

But, only one line can pass through two distinct points.

Here, our supposition ie. l and m have two distinct common points is wrong and theorem ie. two distinct lines cannot have more than one common points has proved.

Proved