2
Question
Two distinct lines have ____ intersecting point(s).
Two distinct lines have ____ intersecting point(s).
Open in App
Solution
The correct option is A 1
Two distinct lines cannot have more than one point in common.
Proof : Suppose there are two given lines l and m. We need to prove that they have only one point in common.
Let us suppose that the two lines intersect in two distinct points,
say A and B. This means we have two lines passing through two distinct points P and Q. But this assumption clashes with the axiom that only one line can pass through two distinct
points. So, the assumption that two lines can pass through two
distinct points is wrong.
So, we conclude that two distinct lines cannot have more than one point in common or tow distinct lines have 1 intersecting point.
Two distinct lines cannot have more than one point in common.
Proof : Suppose there are two given lines l and m. We need to prove that they have only one point in common.
Let us suppose that the two lines intersect in two distinct points,
say A and B. This means we have two lines passing through two distinct points P and Q. But this assumption clashes with the axiom that only one line can pass through two distinct
points. So, the assumption that two lines can pass through two
distinct points is wrong.
So, we conclude that two distinct lines cannot have more than one point in common or tow distinct lines have 1 intersecting point.
Suggest Corrections
2
Similar questions