Lines l and m intersect at a single point K. The proof assumes lines l and m intersect at point K, then shows they cannot intersect at any other point. It states lines l and m intersect at K by given information. It then lets point N be another supposed intersection. But points K and N forming a single line means l and m can only intersect at the single point K.

1. Theorem 1.1
Proof #1

2. Theorem 1.1
• If two distinct lines intersect, then they
intersect in exactly one point.

3. Theorem 1.1
Given
• Lines l and m intersect
at K.
Prove
• They intersect only at
K.
l
m
K

4. Theorem 1.1
Statements Reasons
1 Lines l and m intersect at
K.
Given
2 Let N be an intersection of
l and m
Point-plotting
3 M and N form a line If two distinct points
are given, then a unique
line contains them.
4 Lines l and m intersect
only at K.
Two intersecting lines
never having exactly
two points at common
is impossible.
l
m
K